LMFDB - Embedded newform 143.4.j.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(23,143)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("143.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	143.23
Dual form			143.4.j.a.56.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.60341 + 2.65778i) q^{2} +(3.48806 + 6.04150i) q^{3} +(10.1276 - 17.5415i) q^{4} -11.0780i q^{5} +(-32.1139 - 18.5410i) q^{6} +(-13.4565 - 7.76914i) q^{7} +65.1431i q^{8} +(-10.8331 + 18.7635i) q^{9} +O(q^{10})$	\(q+(-4.60341 + 2.65778i) q^{2} +(3.48806 + 6.04150i) q^{3} +(10.1276 - 17.5415i) q^{4} -11.0780i q^{5} +(-32.1139 - 18.5410i) q^{6} +(-13.4565 - 7.76914i) q^{7} +65.1431i q^{8} +(-10.8331 + 18.7635i) q^{9} +(29.4429 + 50.9966i) q^{10} +(9.52628 - 5.50000i) q^{11} +141.303 q^{12} +(44.5623 + 14.5328i) q^{13} +82.5946 q^{14} +(66.9277 - 38.6407i) q^{15} +(-92.1154 - 159.549i) q^{16} +(-44.7824 + 77.5654i) q^{17} -115.168i q^{18} +(96.4802 + 55.7028i) q^{19} +(-194.325 - 112.194i) q^{20} -108.397i q^{21} +(-29.2356 + 50.6375i) q^{22} +(85.6725 + 148.389i) q^{23} +(-393.562 + 227.223i) q^{24} +2.27774 q^{25} +(-243.763 + 51.5363i) q^{26} +37.2090 q^{27} +(-272.565 + 157.365i) q^{28} +(72.3273 + 125.275i) q^{29} +(-205.397 + 355.758i) q^{30} -253.053i q^{31} +(396.765 + 229.072i) q^{32} +(66.4565 + 38.3687i) q^{33} -476.087i q^{34} +(-86.0666 + 149.072i) q^{35} +(219.427 + 380.058i) q^{36} +(-61.0323 + 35.2370i) q^{37} -592.184 q^{38} +(67.6360 + 319.914i) q^{39} +721.656 q^{40} +(-3.47191 + 2.00451i) q^{41} +(288.095 + 498.995i) q^{42} +(-38.3354 + 66.3988i) q^{43} -222.807i q^{44} +(207.862 + 120.009i) q^{45} +(-788.771 - 455.397i) q^{46} +47.3364i q^{47} +(642.608 - 1113.03i) q^{48} +(-50.7810 - 87.9553i) q^{49} +(-10.4854 + 6.05374i) q^{50} -624.815 q^{51} +(706.236 - 634.507i) q^{52} +537.777 q^{53} +(-171.288 + 98.8933i) q^{54} +(-60.9290 - 105.532i) q^{55} +(506.106 - 876.601i) q^{56} +777.179i q^{57} +(-665.904 - 384.460i) q^{58} +(108.530 + 62.6600i) q^{59} -1565.35i q^{60} +(351.935 - 609.569i) q^{61} +(672.560 + 1164.91i) q^{62} +(291.553 - 168.328i) q^{63} -961.450 q^{64} +(160.995 - 493.661i) q^{65} -407.902 q^{66} +(325.706 - 188.047i) q^{67} +(907.075 + 1571.10i) q^{68} +(-597.662 + 1035.18i) q^{69} -914.984i q^{70} +(414.152 + 239.111i) q^{71} +(-1222.31 - 705.703i) q^{72} +682.809i q^{73} +(187.304 - 324.421i) q^{74} +(7.94490 + 13.7610i) q^{75} +(1954.22 - 1128.27i) q^{76} -170.921 q^{77} +(-1161.62 - 1292.93i) q^{78} -523.488 q^{79} +(-1767.48 + 1020.46i) q^{80} +(422.281 + 731.413i) q^{81} +(10.6551 - 18.4551i) q^{82} -1119.56i q^{83} +(-1901.44 - 1097.80i) q^{84} +(859.270 + 496.100i) q^{85} -407.548i q^{86} +(-504.564 + 873.930i) q^{87} +(358.287 + 620.572i) q^{88} +(-1272.71 + 734.802i) q^{89} -1275.83 q^{90} +(-486.747 - 541.772i) q^{91} +3470.62 q^{92} +(1528.82 - 882.665i) q^{93} +(-125.810 - 217.909i) q^{94} +(617.077 - 1068.81i) q^{95} +3196.07i q^{96} +(251.237 + 145.052i) q^{97} +(467.532 + 269.930i) q^{98} +238.329i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) $ 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25} - 902 q^{26} + 48 q^{27} - 714 q^{28} - 262 q^{29} + 104 q^{30} + 144 q^{32} - 68 q^{35} + 1960 q^{36} + 630 q^{37} - 448 q^{38} - 1612 q^{39} + 216 q^{40} + 126 q^{41} - 82 q^{42} + 436 q^{43} - 570 q^{45} - 1590 q^{46} + 1944 q^{48} + 1192 q^{49} + 1290 q^{50} - 1424 q^{51} + 590 q^{52} + 292 q^{53} - 528 q^{54} - 440 q^{55} - 102 q^{56} - 1128 q^{58} + 504 q^{59} + 590 q^{61} + 1776 q^{62} + 1884 q^{63} - 5028 q^{64} + 994 q^{65} + 2156 q^{66} + 3396 q^{67} + 1530 q^{68} + 12 q^{69} - 1014 q^{71} - 1062 q^{72} - 1568 q^{74} + 4688 q^{75} + 7872 q^{76} - 1232 q^{77} - 4964 q^{78} - 2928 q^{79} - 558 q^{80} - 3780 q^{81} - 4072 q^{82} + 696 q^{84} + 4662 q^{85} + 1832 q^{87} + 924 q^{88} + 1014 q^{89} + 6844 q^{90} + 2900 q^{91} - 1336 q^{92} - 4092 q^{93} + 4166 q^{94} - 256 q^{95} - 5070 q^{97} - 8550 q^{98}+O(q^{100}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.60341	+	2.65778i	−1.62755	+	0.939667i	−0.642731	+	0.766092i	$0.722199\pi$
$2$	−4.60341	+	2.65778i	−1.62755	+	0.939667i	−0.984821	+	0.173575i	$0.944468\pi$
$3$	3.48806	+	6.04150i	0.671277	+	1.16269i	0.977542	+	0.210740i	$0.0675874\pi$
$3$	3.48806	+	6.04150i	0.671277	+	1.16269i	−0.306265	+	0.951946i	$0.599079\pi$
$4$	10.1276	−	17.5415i	1.26595	−	2.19269i
$5$		−	11.0780i		−	0.990847i	−0.868652	−	0.495424i	$-0.835013\pi$
$5$		−	11.0780i		−	0.990847i	0.868652	−	0.495424i	$-0.164987\pi$
$6$	−32.1139	−	18.5410i	−2.18508	−	1.26155i
$7$	−13.4565	−	7.76914i	−0.726585	−	0.419494i	0.0905866	−	0.995889i	$-0.471126\pi$
$7$	−13.4565	−	7.76914i	−0.726585	−	0.419494i	−0.817171	+	0.576395i	$0.804459\pi$
$8$			65.1431i			2.87895i
$9$	−10.8331	+	18.7635i	−0.401227	+	0.694945i
$10$	29.4429	+	50.9966i	0.931067	+	1.61265i
$11$	9.52628	−	5.50000i	0.261116	−	0.150756i
$11$	9.52628	−	5.50000i	0.261116	−	0.150756i
$12$	141.303			3.39921
$13$	44.5623	+	14.5328i	0.950720	+	0.310052i
$13$	44.5623	+	14.5328i	0.950720	+	0.310052i
$14$	82.5946			1.57674
$15$	66.9277	−	38.6407i	1.15204	−	0.665133i
$16$	−92.1154	−	159.549i	−1.43930	−	2.49295i
$17$	−44.7824	+	77.5654i	−0.638901	+	1.10661i	0.346773	+	0.937949i	$0.387278\pi$
$17$	−44.7824	+	77.5654i	−0.638901	+	1.10661i	−0.985674	+	0.168661i	$0.946056\pi$
$18$		−	115.168i		−	1.50808i
$19$	96.4802	+	55.7028i	1.16495	+	0.672585i	0.952485	−	0.304584i	$-0.0985174\pi$
$19$	96.4802	+	55.7028i	1.16495	+	0.672585i	0.212465	+	0.977169i	$0.431851\pi$
$20$	−194.325	−	112.194i	−2.17262	−	1.25436i
$21$		−	108.397i		−	1.12639i
$22$	−29.2356	+	50.6375i	−0.283320	+	0.490725i
$23$	85.6725	+	148.389i	0.776694	+	1.34527i	0.933838	+	0.357697i	$0.116438\pi$
$23$	85.6725	+	148.389i	0.776694	+	1.34527i	−0.157144	+	0.987576i	$0.550229\pi$
$24$	−393.562	+	227.223i	−3.34731	+	1.93257i
$25$	2.27774			0.0182219
$26$	−243.763	+	51.5363i	−1.83869	+	0.388735i
$27$	37.2090			0.265218
$28$	−272.565	+	157.365i	−1.83964	+	1.06212i
$29$	72.3273	+	125.275i	0.463132	+	0.802169i	0.999115	−	0.0420602i	$-0.0133921\pi$
$29$	72.3273	+	125.275i	0.463132	+	0.802169i	−0.535983	+	0.844229i	$0.680059\pi$
$30$	−205.397	+	355.758i	−1.25001	+	2.16508i
$31$		−	253.053i		−	1.46612i	−0.680164	−	0.733060i	$-0.738091\pi$
$31$		−	253.053i		−	1.46612i	0.680164	−	0.733060i	$-0.261909\pi$
$32$	396.765	+	229.072i	2.19184	+	1.26546i
$33$	66.4565	+	38.3687i	0.350563	+	0.202398i
$34$		−	476.087i		−	2.40142i
$35$	−86.0666	+	149.072i	−0.415654	+	0.719935i
$36$	219.427	+	380.058i	1.01586	+	1.75953i
$37$	−61.0323	+	35.2370i	−0.271180	+	0.156566i	−0.629424	−	0.777062i	$-0.716709\pi$
$37$	−61.0323	+	35.2370i	−0.271180	+	0.156566i	0.358244	+	0.933628i	$0.383376\pi$
$38$	−592.184			−2.52802
$39$	67.6360	+	319.914i	0.277703	+	1.31352i
$40$	721.656			2.85260
$41$	−3.47191	+	2.00451i	−0.0132249	+	0.00763540i	−0.506598	−	0.862182i	$-0.669097\pi$
$41$	−3.47191	+	2.00451i	−0.0132249	+	0.00763540i	0.493373	+	0.869818i	$0.335764\pi$
$42$	288.095	+	498.995i	1.05843	+	1.83325i
$43$	−38.3354	+	66.3988i	−0.135956	+	0.235482i	−0.925962	−	0.377616i	$-0.876744\pi$
$43$	−38.3354	+	66.3988i	−0.135956	+	0.235482i	0.790006	+	0.613098i	$0.210077\pi$
$44$		−	222.807i		−	0.763396i
$45$	207.862	+	120.009i	0.688584	+	0.397554i
$46$	−788.771	−	455.397i	−2.52822	−	1.45967i
$47$			47.3364i			0.146909i	0.997299	+	0.0734544i	$0.0234024\pi$
$47$			47.3364i			0.146909i	−0.997299	+	0.0734544i	$0.976598\pi$
$48$	642.608	−	1113.03i	1.93234	−	3.34692i
$49$	−50.7810	−	87.9553i	−0.148050	−	0.256429i
$50$	−10.4854	+	6.05374i	−0.0296571	+	0.0171226i
$51$	−624.815			−1.71552
$52$	706.236	−	634.507i	1.88341	−	1.69212i
$53$	537.777			1.39376			0.696881	−	0.717187i	$-0.254571\pi$
$53$	537.777			1.39376			0.696881	+	0.717187i	$0.254571\pi$
$54$	−171.288	+	98.8933i	−0.431655	+	0.249216i
$55$	−60.9290	−	105.532i	−0.149376	−	0.258727i
$56$	506.106	−	876.601i	1.20770	−	2.09180i
$57$			777.179i			1.80596i
$58$	−665.904	−	384.460i	−1.50754	−	0.870381i
$59$	108.530	+	62.6600i	0.239482	+	0.138265i	0.614939	−	0.788575i	$-0.289181\pi$
$59$	108.530	+	62.6600i	0.239482	+	0.138265i	−0.375457	+	0.926840i	$0.622514\pi$
$60$		−	1565.35i		−	3.36810i
$61$	351.935	−	609.569i	0.738699	−	1.27946i	−0.214382	−	0.976750i	$-0.568774\pi$
$61$	351.935	−	609.569i	0.738699	−	1.27946i	0.953081	−	0.302715i	$-0.0978930\pi$
$62$	672.560	+	1164.91i	1.37767	+	2.38619i
$63$	291.553	−	168.328i	0.583050	−	0.336624i
$64$	−961.450			−1.87783
$65$	160.995	−	493.661i	0.307214	−	0.942018i
$66$	−407.902			−0.760746
$67$	325.706	−	188.047i	0.593901	−	0.342889i	−0.172738	−	0.984968i	$-0.555261\pi$
$67$	325.706	−	188.047i	0.593901	−	0.342889i	0.766638	+	0.642079i	$0.221928\pi$
$68$	907.075	+	1571.10i	1.61763	+	2.80182i
$69$	−597.662	+	1035.18i	−1.04275	+	1.80610i
$70$		−	914.984i		−	1.56231i
$71$	414.152	+	239.111i	0.692265	+	0.399680i	0.804460	−	0.594007i	$-0.202455\pi$
$71$	414.152	+	239.111i	0.692265	+	0.399680i	−0.112195	+	0.993686i	$0.535788\pi$
$72$	−1222.31	−	705.703i	−2.00071	−	1.15511i
$73$			682.809i			1.09475i	0.836887	+	0.547375i	$0.184373\pi$
$73$			682.809i			1.09475i	−0.836887	+	0.547375i	$0.815627\pi$
$74$	187.304	−	324.421i	0.294239	−	0.509637i
$75$	7.94490	+	13.7610i	0.0122320	+	0.0211864i
$76$	1954.22	−	1128.27i	2.94954	−	1.70292i
$77$	−170.921			−0.252964
$78$	−1161.62	−	1292.93i	−1.68625	−	1.87687i
$79$	−523.488			−0.745532			−0.372766	−	0.927925i	$-0.621591\pi$
$79$	−523.488			−0.745532			−0.372766	+	0.927925i	$0.621591\pi$
$80$	−1767.48	+	1020.46i	−2.47013	+	1.42613i
$81$	422.281	+	731.413i	0.579261	+	1.00331i
$82$	10.6551	−	18.4551i	0.0143495	−	0.0248540i
$83$		−	1119.56i		−	1.48058i	−0.672288	−	0.740290i	$-0.734688\pi$
$83$		−	1119.56i		−	1.48058i	0.672288	−	0.740290i	$-0.265312\pi$
$84$	−1901.44	−	1097.80i	−2.46981	−	1.42595i
$85$	859.270	+	496.100i	1.09648	+	0.633054i
$86$		−	407.548i		−	0.511012i
$87$	−504.564	+	873.930i	−0.621781	+	1.07696i
$88$	358.287	+	620.572i	0.434018	+	0.751741i
$89$	−1272.71	+	734.802i	−1.51581	+	0.875155i	−0.515986	+	0.856597i	$0.672574\pi$
$89$	−1272.71	+	734.802i	−1.51581	+	0.875155i	−0.999828	+	0.0185584i	$0.994092\pi$
$90$	−1275.83			−1.49427
$91$	−486.747	−	541.772i	−0.560714	−	0.624100i
$92$	3470.62			3.93302
$93$	1528.82	−	882.665i	1.70464	−	0.984174i
$94$	−125.810	−	217.909i	−0.138045	−	0.239102i
$95$	617.077	−	1068.81i	0.666429	−	1.15429i
$96$			3196.07i			3.39789i
$97$	251.237	+	145.052i	0.262982	+	0.151833i	0.625694	−	0.780068i	$-0.284816\pi$
$97$	251.237	+	145.052i	0.262982	+	0.151833i	−0.362712	+	0.931901i	$0.618149\pi$
$98$	467.532	+	269.930i	0.481917	+	0.278235i
$99$			238.329i			0.241949i
$100$	23.0680	−	39.9550i	0.0230680	−	0.0399550i
$101$	697.868	+	1208.74i	0.687529	+	1.19084i	0.972635	+	0.232339i	$0.0746380\pi$
$101$	697.868	+	1208.74i	0.687529	+	1.19084i	−0.285106	+	0.958496i	$0.592029\pi$
$102$	2876.28	−	1660.62i	2.79210	−	1.61202i
$103$	−474.049			−0.453490			−0.226745	−	0.973954i	$-0.572808\pi$
$103$	−474.049			−0.453490			−0.226745	+	0.973954i	$0.572808\pi$
$104$	−946.713	+	2902.93i	−0.892623	+	2.73707i
$105$	−1200.82			−1.11608
$106$	−2475.61	+	1429.29i	−2.26842	+	1.30967i
$107$	−537.463	−	930.913i	−0.485594	−	0.841073i	0.514269	−	0.857629i	$-0.328063\pi$
$107$	−537.463	−	930.913i	−0.485594	−	0.841073i	−0.999863	+	0.0165561i	$0.994730\pi$
$108$	376.837	−	652.702i	0.335752	−	0.581539i
$109$			850.721i			0.747562i	0.927517	+	0.373781i	$0.121939\pi$
$109$			850.721i			0.747562i	−0.927517	+	0.373781i	$0.878061\pi$
$110$	560.963	+	323.872i	0.486234	+	0.280727i
$111$	−425.768	−	245.818i	−0.364073	−	0.210198i
$112$			2862.63i			2.41512i
$113$	−655.346	+	1135.09i	−0.545573	+	0.944960i	0.452997	+	0.891512i	$0.350355\pi$
$113$	−655.346	+	1135.09i	−0.545573	+	0.944960i	−0.998571	+	0.0534486i	$0.982979\pi$
$114$	−2065.57	−	3577.68i	−1.69700	−	2.93930i
$115$	1643.86	−	949.081i	1.33296	−	0.769585i
$116$	2930.00			2.34521
$117$	−755.435	+	678.709i	−0.596923	+	0.536297i
$118$	−666.146			−0.519693
$119$	1205.23	−	695.841i	0.928432	−	0.536031i
$120$	2517.18	+	4359.88i	1.91488	+	3.31668i
$121$	60.5000	−	104.789i	0.0454545	−	0.0787296i
$122$			3741.46i			2.77653i
$123$	−24.2205	−	13.9837i	−0.0177552	−	0.0102509i
$124$	−4438.94	−	2562.82i	−3.21474	−	1.85603i
$125$		−	1409.98i		−	1.00890i
$126$	−894.757	+	1549.76i	−0.632629	+	1.09575i
$127$	−55.7773	−	96.6092i	−0.0389719	−	0.0675014i	0.845882	−	0.533371i	$-0.179075\pi$
$127$	−55.7773	−	96.6092i	−0.0389719	−	0.0675014i	−0.884853	+	0.465869i	$0.845742\pi$
$128$	1251.83	−	722.744i	0.864431	−	0.499079i
$129$	−534.864			−0.365056
$130$	570.919	+	2700.41i	0.385177	+	1.82186i
$131$	−1915.22			−1.27735			−0.638677	−	0.769475i	$-0.720518\pi$
$131$	−1915.22			−1.27735			−0.638677	+	0.769475i	$0.720518\pi$
$132$	1346.09	−	777.164i	0.887590	−	0.512450i
$133$	−865.526	−	1499.14i	−0.564290	−	0.977380i
$134$	−999.573	+	1731.31i	−0.644403	+	1.11614i
$135$		−	412.202i		−	0.262790i
$136$	−5052.85	−	2917.27i	−3.18587	−	1.83936i
$137$	−1153.17	−	665.782i	−0.719137	−	0.415194i	0.0952980	−	0.995449i	$-0.469620\pi$
$137$	−1153.17	−	665.782i	−0.719137	−	0.415194i	−0.814435	+	0.580255i	$0.802953\pi$
$138$		−	6353.81i		−	3.91937i
$139$	360.632	−	624.633i	0.220060	−	0.381156i	−0.734766	−	0.678321i	$-0.762708\pi$
$139$	360.632	−	624.633i	0.220060	−	0.381156i	0.954826	+	0.297165i	$0.0960412\pi$
$140$	1743.29	+	3019.47i	1.05239	+	1.82280i
$141$	−285.982	+	165.112i	−0.170809	+	0.0986166i
$142$	−2542.02			−1.50226
$143$	504.443	−	106.649i	0.294991	−	0.0623667i
$144$	3991.59			2.30995
$145$	1387.79	−	801.242i	0.794827	−	0.458893i
$146$	−1814.76	−	3143.25i	−1.02870	−	1.78176i
$147$	354.254	−	613.587i	0.198765	−	0.344271i
$148$			1427.46i			0.792816i
$149$	147.226	+	85.0010i	0.0809479	+	0.0467353i	0.539928	−	0.841711i	$-0.318452\pi$
$149$	147.226	+	85.0010i	0.0809479	+	0.0467353i	−0.458980	+	0.888447i	$0.651785\pi$
$150$	−73.1473	−	42.2316i	−0.0398163	−	0.0229880i
$151$		−	1479.84i		−	0.797535i	−0.917052	−	0.398768i	$-0.869438\pi$
$151$		−	1479.84i		−	0.797535i	0.917052	−	0.398768i	$-0.130562\pi$
$152$	−3628.66	+	6285.02i	−1.93634	+	3.35383i
$153$	−970.266	−	1680.55i	−0.512688	−	0.888002i
$154$	786.820	−	454.270i	0.411712	−	0.237702i
$155$	−2803.33			−1.45270
$156$	6296.76	+	2053.52i	3.23170	+	1.05393i
$157$	3644.27			1.85251			0.926255	−	0.376897i	$-0.123009\pi$
$157$	3644.27			1.85251			0.926255	+	0.376897i	$0.123009\pi$
$158$	2409.83	−	1391.32i	1.21339	−	0.700552i
$159$	1875.80	+	3248.98i	0.935601	+	1.62051i
$160$	2537.67	−	4395.37i	1.25388	−	2.17178i
$161$		−	2662.41i		−	1.30327i
$162$	−3887.87	−	2244.66i	−1.88555	−	1.08863i
$163$	1375.84	+	794.342i	0.661130	+	0.381703i	0.792707	−	0.609602i	$-0.208671\pi$
$163$	1375.84	+	794.342i	0.661130	+	0.381703i	−0.131578	+	0.991306i	$0.542004\pi$
$164$			81.2033i			0.0386641i
$165$	425.048	−	736.205i	0.200545	−	0.347354i
$166$	2975.56	+	5153.81i	1.39125	+	2.40972i
$167$	−2519.09	+	1454.40i	−1.16726	+	0.673920i	−0.953034	−	0.302863i	$-0.902057\pi$
$167$	−2519.09	+	1454.40i	−1.16726	+	0.673920i	−0.214230	+	0.976783i	$0.568724\pi$
$168$	7061.31			3.24281
$169$	1774.60	+	1295.23i	0.807736	+	0.589545i
$170$	−5274.10			−2.37944
$171$	−2090.36	+	1206.87i	−0.934818	+	0.539718i
$172$	776.490	+	1344.92i	0.344226	+	0.596216i
$173$	1992.55	−	3451.20i	0.875670	−	1.51670i	0.0196227	−	0.999807i	$-0.493754\pi$
$173$	1992.55	−	3451.20i	0.875670	−	1.51670i	0.856047	−	0.516897i	$-0.172913\pi$
$174$		−	5364.08i		−	2.33707i
$175$	−30.6505	−	17.6961i	−0.0132398	−	0.00764400i
$176$	−1755.03	−	1013.27i	−0.751652	−	0.433966i
$177$			874.247i			0.371257i
$178$	3905.88	−	6765.19i	1.64471	−	2.84872i
$179$	−679.028	−	1176.11i	−0.283536	−	0.491099i	0.688717	−	0.725030i	$-0.258174\pi$
$179$	−679.028	−	1176.11i	−0.283536	−	0.491099i	−0.972253	+	0.233931i	$0.924841\pi$
$180$	4210.29	−	2430.81i	1.74342	−	1.00657i
$181$	−1239.66			−0.509080			−0.254540	−	0.967062i	$-0.581924\pi$
$181$	−1239.66			−0.509080			−0.254540	+	0.967062i	$0.581924\pi$
$182$	3680.61	+	1200.33i	1.49904	+	0.488871i
$183$	4910.28			1.98349
$184$	−9666.53	+	5580.98i	−3.87297	+	2.23606i
$185$	390.356	+	676.116i	0.155133	+	0.268698i
$186$	−4691.86	+	8126.54i	−1.84959	+	3.20359i
$187$			985.213i			0.385272i
$188$	830.351	+	479.403i	0.322125	+	0.185979i
$189$	−500.704	−	289.082i	−0.192703	−	0.111257i
$190$			6560.21i			2.50488i
$191$	−1827.12	+	3164.66i	−0.692176	+	1.19888i	0.278947	+	0.960306i	$0.410015\pi$
$191$	−1827.12	+	3164.66i	−0.692176	+	1.19888i	−0.971123	+	0.238578i	$0.923319\pi$
$192$	−3353.60	−	5808.60i	−1.26055	−	2.18333i
$193$	−1364.18	+	787.609i	−0.508786	+	0.293748i	−0.732334	−	0.680945i	$-0.761569\pi$
$193$	−1364.18	+	787.609i	−0.508786	+	0.293748i	0.223549	+	0.974693i	$0.428236\pi$
$194$	−1542.06			−0.570689
$195$	3544.01	−	749.272i	1.30150	−	0.275162i
$196$	−2057.16			−0.749693
$197$	2816.88	−	1626.33i	1.01875	−	0.588177i	0.105011	−	0.994471i	$-0.466512\pi$
$197$	2816.88	−	1626.33i	1.01875	−	0.588177i	0.913743	+	0.406294i	$0.133179\pi$
$198$	−633.425	−	1097.12i	−0.227351	−	0.393784i
$199$	2214.37	−	3835.40i	0.788807	−	1.36625i	−0.137891	−	0.990447i	$-0.544032\pi$
$199$	2214.37	−	3835.40i	0.788807	−	1.36625i	0.926698	−	0.375806i	$-0.122634\pi$
$200$			148.379i			0.0524600i
$201$	2272.17	+	1311.84i	0.797344	+	0.460347i
$202$	−6425.14	−	3709.56i	−2.23798	−	1.29210i
$203$		−	2247.68i		−	0.777125i
$204$	−6327.87	+	10960.2i	−2.17176	+	3.76160i
$205$	22.2060	+	38.4618i	0.00756552	+	0.0131039i
$206$	2182.24	−	1259.92i	0.738078	−	0.426129i
$207$	−3712.40			−1.24652
$208$	−1786.19	−	8448.55i	−0.595431	−	2.81635i
$209$	1225.46			0.405584
$210$	5527.87	−	3191.52i	1.81647	−	1.04874i
$211$	−1720.79	−	2980.50i	−0.561443	−	0.972447i	−0.997371	−	0.0724658i	$-0.976913\pi$
$211$	−1720.79	−	2980.50i	−0.561443	−	0.972447i	0.435928	−	0.899981i	$-0.356420\pi$
$212$	5446.39	−	9433.42i	1.76443	−	3.05608i
$213$			3336.13i			1.07318i
$214$	4948.32	+	2856.92i	1.58066	+	0.912593i
$215$	735.567	+	424.680i	0.233327	+	0.134711i
$216$			2423.91i			0.763547i
$217$	−1966.01	+	3405.22i	−0.615029	+	1.06526i
$218$	−2261.03	−	3916.22i	−0.702460	−	1.21670i
$219$	−4125.19	+	2381.68i	−1.27285	+	0.734881i
$220$	−2468.26			−0.756409
$221$	−3122.85	+	2805.68i	−0.950523	+	0.853983i
$222$	2613.32			0.790064
$223$	−4228.24	+	2441.18i	−1.26970	+	0.733064i	−0.974932	−	0.222503i	$-0.928577\pi$
$223$	−4228.24	+	2441.18i	−1.26970	+	0.733064i	−0.294772	+	0.955567i	$0.595244\pi$
$224$	−3559.39	−	6165.05i	−1.06170	−	1.83893i
$225$	−24.6751	+	42.7384i	−0.00731113	+	0.0126632i
$226$		−	6967.06i		−	2.05063i
$227$	473.558	+	273.409i	0.138463	+	0.0799418i	0.567631	−	0.823283i	$-0.307860\pi$
$227$	473.558	+	273.409i	0.138463	+	0.0799418i	−0.429168	+	0.903225i	$0.641193\pi$
$228$	13632.9	+	7870.95i	3.95991	+	2.28626i
$229$			5874.05i			1.69506i	0.530750	+	0.847529i	$0.321910\pi$
$229$			5874.05i			1.69506i	−0.530750	+	0.847529i	$0.678090\pi$
$230$	−5044.90	+	8738.01i	−1.44631	+	2.50508i
$231$	−596.183	−	1032.62i	−0.169809	−	0.294118i
$232$	−8160.78	+	4711.63i	−2.30940	+	1.33333i
$233$	−1049.73			−0.295151			−0.147575	−	0.989051i	$-0.547147\pi$
$233$	−1049.73			−0.295151			−0.147575	+	0.989051i	$0.547147\pi$
$234$	1673.72	−	5132.16i	0.467582	−	1.43376i
$235$	524.393			0.145564
$236$	2198.30	−	1269.19i	0.606344	−	0.350073i
$237$	−1825.96	−	3162.65i	−0.500459	−	0.866820i
$238$	−3698.78	+	6406.48i	−1.00738	+	1.74483i
$239$			243.032i			0.0657758i	0.999459	+	0.0328879i	$0.0104704\pi$
$239$			243.032i			0.0657758i	−0.999459	+	0.0328879i	$0.989530\pi$
$240$	−12330.2	−	7118.82i	−3.31628	−	1.91466i
$241$	599.177	+	345.935i	0.160151	+	0.0924633i	0.577934	−	0.816084i	$-0.303859\pi$
$241$	599.177	+	345.935i	0.160151	+	0.0924633i	−0.417783	+	0.908547i	$0.637193\pi$
$242$			643.183i			0.170849i
$243$	−2443.56	+	4232.38i	−0.645081	+	1.11731i
$244$	−7128.51	−	12346.9i	−1.87031	−	3.23947i
$245$	−974.370	+	562.553i	−0.254082	+	0.146695i
$246$	148.662			0.0385299
$247$	3489.86	+	3884.37i	0.899005	+	1.00063i
$248$	16484.7			4.22088
$249$	6763.84	−	3905.11i	1.72145	−	0.993880i
$250$	3747.43	+	6490.73i	0.948032	+	1.64204i
$251$	991.283	−	1716.95i	0.249280	−	0.431765i	−0.714046	−	0.700098i	$-0.753139\pi$
$251$	991.283	−	1716.95i	0.249280	−	0.431765i	0.963326	+	0.268333i	$0.0864728\pi$
$252$		−	6819.02i		−	1.70460i
$253$	1632.28	+	942.398i	0.405615	+	0.234182i
$254$	513.532	+	296.488i	0.126858	+	0.0732413i
$255$			6921.70i			1.69982i
$256$	4.01334	−	6.95132i	0.000979820	−	0.00169710i
$257$	−2866.01	−	4964.07i	−0.695629	−	1.20486i	−0.969968	−	0.243231i	$-0.921793\pi$
$257$	−2866.01	−	4964.07i	−0.695629	−	1.20486i	0.274340	−	0.961633i	$-0.411541\pi$
$258$	2462.20	−	1421.55i	0.594147	−	0.343031i
$259$	1095.04			0.262713
$260$	−7029.07	−	7823.69i	−1.67663	−	1.86617i
$261$	−3134.12			−0.743284
$262$	8816.53	−	5090.22i	2.07896	−	1.20029i
$263$	−127.942	−	221.602i	−0.0299971	−	0.0519564i	0.850637	−	0.525753i	$-0.176216\pi$
$263$	−127.942	−	221.602i	−0.0299971	−	0.0519564i	−0.880634	+	0.473797i	$0.842883\pi$
$264$	−2499.45	+	4329.18i	−0.582692	+	1.00925i
$265$		−	5957.50i		−	1.38100i
$266$	7968.74	+	4600.76i	1.83682	+	1.06049i
$267$	−8878.60	−	5126.06i	−2.03506	−	1.17494i
$268$		−	7617.84i		−	1.73632i
$269$	2996.18	−	5189.54i	0.679109	−	1.17625i	−0.296140	−	0.955144i	$-0.595700\pi$
$269$	2996.18	−	5189.54i	0.679109	−	1.17625i	0.975250	−	0.221107i	$-0.0709670\pi$
$270$	1095.54	+	1897.53i	0.246935	+	0.427704i
$271$	−6068.00	+	3503.36i	−1.36017	+	0.785292i	−0.989646	−	0.143532i	$-0.954154\pi$
$271$	−6068.00	+	3503.36i	−1.36017	+	0.785292i	−0.370520	+	0.928824i	$0.620821\pi$
$272$	16500.6			3.67829
$273$	1575.31	−	4830.41i	0.349239	−	1.07088i
$274$	7078.00			1.56058
$275$	21.6984	−	12.5276i	0.00475805	−	0.00274706i
$276$	12105.7	+	20967.8i	2.64014	+	4.57287i
$277$	−3274.80	+	5672.12i	−0.710338	+	1.23034i	0.254393	+	0.967101i	$0.418124\pi$
$277$	−3274.80	+	5672.12i	−0.710338	+	1.23034i	−0.964730	+	0.263240i	$0.915209\pi$
$278$			3833.92i			0.827134i
$279$	4748.17	+	2741.36i	1.01887	+	0.588247i
$280$	−9711.00	−	5606.65i	−2.07265	−	1.19665i
$281$		−	3408.41i		−	0.723589i	−0.932258	−	0.361795i	$-0.882164\pi$
$281$		−	3408.41i		−	0.723589i	0.932258	−	0.361795i	$-0.117836\pi$
$282$	877.663	−	1520.16i	0.185334	−	0.321007i
$283$	−952.472	−	1649.73i	−0.200066	−	0.346524i	0.748484	−	0.663153i	$-0.230782\pi$
$283$	−952.472	−	1649.73i	−0.200066	−	0.346524i	−0.948549	+	0.316629i	$0.897449\pi$
$284$	8388.73	−	4843.23i	1.75274	−	1.01195i
$285$	8609.60			1.78943
$286$	−2038.71	+	1831.65i	−0.421508	+	0.378698i
$287$	62.2932			0.0128120
$288$	−8596.41	+	4963.14i	−1.75885	+	1.01547i
$289$	−1554.43	−	2692.34i	−0.316390	−	0.548004i
$290$	−4259.05	+	7376.89i	−0.862414	+	1.49375i
$291$			2023.80i			0.407688i
$292$	11977.5	+	6915.21i	2.40045	+	1.38590i
$293$	−3036.25	−	1752.98i	−0.605391	−	0.349523i	0.165768	−	0.986165i	$-0.446990\pi$
$293$	−3036.25	−	1752.98i	−0.605391	−	0.349523i	−0.771159	+	0.636642i	$0.780323\pi$
$294$			3766.12i			0.747091i
$295$	694.148	−	1202.30i	0.137000	−	0.237290i
$296$	−2295.45	−	3975.83i	−0.450744	−	0.780712i
$297$	354.463	−	204.649i	0.0692527	−	0.0399831i
$298$	−903.656			−0.175662
$299$	1661.25	+	7857.62i	0.321313	+	1.51979i
$300$	321.851			0.0619402
$301$	1031.72	−	595.666i	0.197567	−	0.114065i
$302$	3933.09	+	6812.32i	0.749418	+	1.29803i
$303$	−4868.41	+	8432.33i	−0.923045	+	1.59876i
$304$		−	20524.4i		−	3.87221i
$305$	−6752.81	−	3898.74i	−1.26775	−	0.731938i
$306$	8933.06	+	5157.51i	1.66885	+	0.963513i
$307$		−	2184.20i		−	0.406055i	−0.979173	−	0.203027i	$-0.934922\pi$
$307$		−	2184.20i		−	0.406055i	0.979173	−	0.203027i	$-0.0650781\pi$
$308$	−1731.02	+	2998.21i	−0.320240	+	0.554672i
$309$	−1653.51	−	2863.97i	−0.304417	−	0.527266i
$310$	12904.9	−	7450.63i	2.36435	−	1.36506i
$311$	3040.19			0.554319			0.277159	−	0.960824i	$-0.410607\pi$
$311$	3040.19			0.554319			0.277159	+	0.960824i	$0.410607\pi$
$312$	−20840.2	+	4406.02i	−3.78155	+	0.799493i
$313$	−4697.28			−0.848261			−0.424131	−	0.905601i	$-0.639420\pi$
$313$	−4697.28			−0.848261			−0.424131	+	0.905601i	$0.639420\pi$
$314$	−16776.1	+	9685.66i	−3.01506	+	1.74074i
$315$	−1864.74	−	3229.82i	−0.333543	−	0.577714i
$316$	−5301.67	+	9182.77i	−0.943805	+	1.63472i
$317$			3645.08i			0.645830i	0.946428	+	0.322915i	$0.104663\pi$
$317$			3645.08i			0.645830i	−0.946428	+	0.322915i	$0.895337\pi$
$318$	−17270.1	−	9970.92i	−3.04548	−	1.75831i
$319$	1378.02	+	795.600i	0.241863	+	0.139640i
$320$			10651.0i			1.86065i
$321$	3749.41	−	6494.16i	0.651936	−	1.12919i
$322$	7076.09	+	12256.1i	1.22464	+	2.12114i
$323$	−8641.22	+	4989.01i	−1.48858	+	0.859431i
$324$	17106.8			2.93326
$325$	101.501	+	33.1020i	0.0173240	+	0.00564975i
$326$	−8444.75			−1.43470
$327$	−5139.63	+	2967.37i	−0.869181	+	0.501822i
$328$	−130.580	−	226.171i	−0.0219819	−	0.0380738i
$329$	367.763	−	636.984i	0.0616274	−	0.106742i
$330$			4518.74i			0.753783i
$331$	303.744	+	175.366i	0.0504388	+	0.0291209i	0.525007	−	0.851098i	$-0.324063\pi$
$331$	303.744	+	175.366i	0.0504388	+	0.0291209i	−0.474569	+	0.880219i	$0.657396\pi$
$332$	−19638.8	−	11338.5i	−3.24645	−	1.87434i
$333$		−	1526.91i		−	0.251273i
$334$	7730.94	−	13390.4i	1.26652	−	2.19368i
$335$	−2083.18	−	3608.18i	−0.339750	−	0.588465i
$336$	−17294.6	+	9985.02i	−2.80802	+	1.62121i
$337$	−1941.68			−0.313858			−0.156929	−	0.987610i	$-0.550159\pi$
$337$	−1941.68			−0.313858			−0.156929	+	0.987610i	$0.550159\pi$
$338$	−11611.6	−	1245.99i	−1.86861	−	0.200512i
$339$	−9143.54			−1.46492
$340$	17404.7	−	10048.6i	2.77618	−	1.60283i
$341$	−1391.79	−	2410.66i	−0.221026	−	0.382828i
$342$	6415.19	−	11111.4i	1.01431	−	1.75684i
$343$			6907.73i			1.08741i
$344$	−4325.43	−	2497.29i	−0.677940	−	0.391409i
$345$	11467.7	+	6620.90i	1.78957	+	1.03321i
$346$			21183.1i			3.29135i
$347$	1553.26	−	2690.32i	0.240298	−	0.416208i	−0.720501	−	0.693454i	$-0.756088\pi$
$347$	1553.26	−	2690.32i	0.240298	−	0.416208i	0.960799	+	0.277246i	$0.0894216\pi$
$348$	10220.0	+	17701.6i	1.57428	+	2.72674i
$349$	7766.33	−	4483.89i	1.19118	−	0.687728i	0.232606	−	0.972571i	$-0.425275\pi$
$349$	7766.33	−	4483.89i	1.19118	−	0.687728i	0.958574	+	0.284843i	$0.0919414\pi$
$350$	188.129			0.0287312
$351$	1658.12	+	540.751i	0.252148	+	0.0822312i
$352$	5039.59			0.763100
$353$	464.202	−	268.007i	0.0699915	−	0.0404096i	−0.464596	−	0.885523i	$-0.653800\pi$
$353$	464.202	−	268.007i	0.0699915	−	0.0404096i	0.534587	+	0.845113i	$0.320467\pi$
$354$	−2323.56	−	4024.52i	−0.348858	−	0.604240i
$355$	2648.87	−	4587.98i	0.396021	−	0.685929i
$356$			29767.1i			4.43161i
$357$	8407.84	+	4854.27i	1.24647	+	0.719650i
$358$	6251.69	+	3609.42i	0.922939	+	0.532859i
$359$		−	6395.52i		−	0.940231i	−0.882605	−	0.470115i	$-0.844212\pi$
$359$		−	6395.52i		−	0.940231i	0.882605	−	0.470115i	$-0.155788\pi$
$360$	−7817.79	+	13540.8i	−1.14454	+	1.98240i
$361$	2776.11	+	4808.37i	0.404740	+	0.701031i
$362$	5706.68	−	3294.75i	0.828554	−	0.478366i
$363$	844.110			0.122050
$364$	−14433.1	+	3051.43i	−2.07829	+	0.439391i
$365$	7564.17			1.08473
$366$	−22604.0	+	13050.4i	−3.22823	+	1.86382i
$367$	2012.47	+	3485.70i	0.286240	+	0.495783i	0.972909	−	0.231188i	$-0.0742611\pi$
$367$	2012.47	+	3485.70i	0.286240	+	0.495783i	−0.686669	+	0.726970i	$0.740928\pi$
$368$	15783.5	−	27337.9i	2.23580	−	3.87251i
$369$		−	86.8603i		−	0.0122541i
$370$	−3593.94	−	2074.96i	−0.504973	−	0.291546i
$371$	−7236.62	−	4178.06i	−1.01269	−	0.584675i
$372$		−	35757.1i		−	4.98365i
$373$	5427.20	−	9400.19i	0.753378	−	1.30489i	−0.192799	−	0.981238i	$-0.561756\pi$
$373$	5427.20	−	9400.19i	0.753378	−	1.30489i	0.946177	−	0.323650i	$-0.104910\pi$
$374$	−2618.48	−	4535.34i	−0.362028	−	0.627050i
$375$	8518.41	−	4918.11i	1.17304	−	0.677253i
$376$	−3083.64			−0.422943
$377$	1402.48	+	6633.64i	0.191595	+	0.906233i
$378$	3073.26			0.418179
$379$	2032.08	−	1173.22i	0.275411	−	0.159008i	−0.355933	−	0.934511i	$-0.615837\pi$
$379$	2032.08	−	1173.22i	0.275411	−	0.159008i	0.631344	+	0.775503i	$0.282504\pi$
$380$	−12499.0	−	21648.9i	−1.68733	−	2.92254i
$381$	389.109	−	673.957i	0.0523220	−	0.0906243i
$382$		−	19424.3i		−	2.60166i
$383$	−582.765	−	336.460i	−0.0777491	−	0.0448885i	0.460621	−	0.887597i	$-0.347627\pi$
$383$	−582.765	−	336.460i	−0.0777491	−	0.0448885i	−0.538371	+	0.842708i	$0.680960\pi$
$384$	8732.91	+	5041.95i	1.16055	+	0.670041i
$385$			1893.46i			0.250649i
$386$	4186.58	−	7251.37i	0.552050	−	0.956179i
$387$	−830.583	−	1438.61i	−0.109098	−	0.188963i
$388$	5088.85	−	2938.05i	0.665844	−	0.384425i
$389$	6019.15			0.784532			0.392266	−	0.919852i	$-0.371691\pi$
$389$	6019.15			0.784532			0.392266	+	0.919852i	$0.371691\pi$
$390$	−14323.1	+	12868.4i	−1.85969	+	1.67081i
$391$	−15346.5			−1.98492
$392$	5729.68	−	3308.04i	0.738247	−	0.426227i
$393$	−6680.39	−	11570.8i	−0.857458	−	1.48516i
$394$	−8644.84	+	14973.3i	−1.10538	+	1.91458i
$395$			5799.21i			0.738708i
$396$	4180.64	+	2413.69i	0.530518	+	0.306295i
$397$	1042.64	+	601.966i	0.131810	+	0.0761003i	0.564455	−	0.825464i	$-0.309086\pi$
$397$	1042.64	+	601.966i	0.131810	+	0.0761003i	−0.432645	+	0.901564i	$0.642420\pi$
$398$			23541.2i			2.96486i
$399$	6038.01	−	10458.1i	0.757591	−	1.31219i
$400$	−209.815	−	363.411i	−0.0262269	−	0.0454263i
$401$	2620.24	−	1512.80i	0.326306	−	0.188393i	−0.327894	−	0.944715i	$-0.606339\pi$
$401$	2620.24	−	1512.80i	0.326306	−	0.188393i	0.654200	+	0.756322i	$0.273006\pi$
$402$	−13946.3			−1.73029
$403$	3677.58	−	11276.6i	0.454574	−	1.39387i
$404$	28270.9			3.48151
$405$	8102.60	−	4678.04i	0.994126	−	0.573959i
$406$	5973.84	+	10347.0i	0.730239	+	1.26481i
$407$	−387.607	+	671.355i	−0.0472063	+	0.0817637i
$408$		−	40702.4i		−	4.93889i
$409$	1063.07	+	613.765i	0.128522	+	0.0742023i	0.562883	−	0.826537i	$-0.309692\pi$
$409$	1063.07	+	613.765i	0.128522	+	0.0742023i	−0.434361	+	0.900739i	$0.643026\pi$
$410$	−204.446	−	118.037i	−0.0246265	−	0.0142181i
$411$		−	9289.14i		−	1.11484i
$412$	−4800.97	+	8315.53i	−0.574095	+	0.994361i
$413$	−973.629	−	1686.37i	−0.116003	−	0.200923i
$414$	17089.7	−	9866.74i	2.02878	−	1.17131i
$415$	−12402.5			−1.46703
$416$	14351.7	+	15974.1i	1.69147	+	1.88268i
$417$	5031.62			0.590886
$418$	−5641.31	+	3257.01i	−0.660108	+	0.381114i
$419$	2729.32	+	4727.31i	0.318224	+	0.551180i	0.980118	−	0.198418i	$-0.0635803\pi$
$419$	2729.32	+	4727.31i	0.318224	+	0.551180i	−0.661894	+	0.749598i	$0.730247\pi$
$420$	−12161.4	+	21064.2i	−1.41290	+	2.44721i
$421$			5108.50i			0.591385i	0.955283	+	0.295693i	$0.0955505\pi$
$421$			5108.50i			0.591385i	−0.955283	+	0.295693i	$0.904450\pi$
$422$	15843.0	+	9146.99i	1.82755	+	1.05514i
$423$	−888.196	−	512.800i	−0.102094	−	0.0589437i
$424$			35032.5i			4.01257i
$425$	−102.003	+	176.674i	−0.0116420	+	0.0201646i
$426$	−8866.71	−	15357.6i	−1.00843	−	1.74666i
$427$	−9471.66	+	5468.46i	−1.07346	+	0.619760i
$428$	−21772.8			−2.45895
$429$	2403.85	+	2675.59i	0.270533	+	0.301116i
$430$	−4514.82			−0.506335
$431$	5381.02	−	3106.73i	0.601379	−	0.347207i	−0.168205	−	0.985752i	$-0.553797\pi$
$431$	5381.02	−	3106.73i	0.601379	−	0.347207i	0.769584	+	0.638546i	$0.220464\pi$
$432$	−3427.52	−	5936.64i	−0.381729	−	0.661173i
$433$	−1969.53	+	3411.33i	−0.218591	+	0.378610i	−0.954377	−	0.298603i	$-0.903479\pi$
$433$	−1969.53	+	3411.33i	−0.218591	+	0.378610i	0.735787	+	0.677213i	$0.236813\pi$
$434$		−	20900.9i		−	2.31169i
$435$	9681.40	+	5589.56i	1.06710	+	0.616089i
$436$	14922.9	+	8615.75i	1.63917	+	0.946376i
$437$			19088.8i			2.08957i
$438$	12660.0	−	21927.7i	1.38109	−	2.39211i
$439$	1530.69	+	2651.22i	0.166414	+	0.288237i	0.937156	−	0.348910i	$-0.113448\pi$
$439$	1530.69	+	2651.22i	0.166414	+	0.288237i	−0.770743	+	0.637146i	$0.780115\pi$
$440$	6874.70	−	3969.11i	0.744860	−	0.430045i
$441$	2200.47			0.237606
$442$	6918.88	−	21215.5i	0.744565	−	2.28308i
$443$	−13006.8			−1.39497			−0.697487	−	0.716598i	$-0.745698\pi$
$443$	−13006.8			−1.39497			−0.697487	+	0.716598i	$0.745698\pi$
$444$	−8624.02	+	4979.08i	−0.921797	+	0.532200i
$445$	8140.14	+	14099.1i	0.867145	+	1.50194i
$446$	12976.2	−	22475.5i	1.37767	−	2.38620i
$447$			1185.95i			0.125489i
$448$	12937.8	+	7469.64i	1.36440	+	0.787740i
$449$	−10785.5	−	6227.01i	−1.13363	−	0.654501i	−0.188784	−	0.982019i	$-0.560455\pi$
$449$	−10785.5	−	6227.01i	−1.13363	−	0.654501i	−0.944845	+	0.327518i	$0.893788\pi$
$450$		−	262.323i		−	0.0274801i
$451$	−22.0496	+	38.1910i	−0.00230216	+	0.00398746i
$452$	13274.1	+	22991.5i	1.38134	+	2.39254i
$453$	8940.46	−	5161.78i	0.927284	−	0.535367i
$454$	−2906.64			−0.300475
$455$	−6001.75	+	5392.19i	−0.618388	+	0.555581i
$456$	−50627.9			−5.19927
$457$	10123.0	−	5844.52i	1.03618	−	0.598239i	0.117431	−	0.993081i	$-0.462534\pi$
$457$	10123.0	−	5844.52i	1.03618	−	0.598239i	0.918749	+	0.394842i	$0.129201\pi$
$458$	−15611.9	−	27040.7i	−1.59279	−	2.75879i
$459$	−1666.31	+	2886.13i	−0.169448	+	0.293492i
$460$		−	38447.6i		−	3.89702i
$461$	−12580.6	−	7263.40i	−1.27101	−	0.733819i	−0.295833	−	0.955240i	$-0.595597\pi$
$461$	−12580.6	−	7263.40i	−1.27101	−	0.733819i	−0.975178	+	0.221421i	$0.928931\pi$
$462$	5488.95	+	3169.04i	0.552747	+	0.319128i
$463$		−	5591.84i		−	0.561284i	−0.959812	−	0.280642i	$-0.909453\pi$
$463$		−	5591.84i		−	0.561284i	0.959812	−	0.280642i	$-0.0905474\pi$
$464$	13324.9	−	23079.4i	1.33318	−	2.30913i
$465$	−9778.17	−	16936.3i	−0.975166	−	1.68904i
$466$	4832.34	−	2789.95i	0.480373	−	0.277344i
$467$	−9034.52			−0.895220			−0.447610	−	0.894229i	$-0.647725\pi$
$467$	−9034.52			−0.895220			−0.447610	+	0.894229i	$0.647725\pi$
$468$	4254.84	+	20125.1i	0.420257	+	1.98779i
$469$	−5843.84			−0.575359
$470$	−2413.99	+	1393.72i	−0.236913	+	0.136782i
$471$	12711.4	+	22016.8i	1.24355	+	2.15389i
$472$	−4081.87	+	7070.01i	−0.398058	+	0.689456i
$473$			843.379i			0.0819843i
$474$	16811.3	+	9705.99i	1.62904	+	0.940529i
$475$	219.757	+	126.877i	0.0212277	+	0.0122558i
$476$		−	28188.8i		−	2.71435i
$477$	−5825.80	+	10090.6i	−0.559214	+	0.968587i
$478$	−645.925	−	1118.77i	−0.0618074	−	0.107053i
$479$	−2961.64	+	1709.91i	−0.282507	+	0.163106i	−0.634558	−	0.772875i	$-0.718818\pi$
$479$	−2961.64	+	1709.91i	−0.282507	+	0.163106i	0.352051	+	0.935981i	$0.385484\pi$
$480$	35406.1			3.36679
$481$	−3231.83	+	683.271i	−0.306359	+	0.0647702i
$482$	−3677.68			−0.347539
$483$	16084.9	−	9286.63i	1.51530	−	0.874858i
$484$	−1225.44	−	2122.52i	−0.115086	−	0.199335i
$485$	1606.89	−	2783.21i	0.150443	−	0.260575i
$486$		−	25977.8i		−	2.42465i
$487$	−8416.06	−	4859.01i	−0.783096	−	0.452121i	0.0544302	−	0.998518i	$-0.482666\pi$
$487$	−8416.06	−	4859.01i	−0.783096	−	0.452121i	−0.837526	+	0.546397i	$0.815999\pi$
$488$	39709.3	+	22926.2i	3.68351	+	2.12668i
$489$			11082.8i			1.02492i
$490$	2990.28	−	5179.32i	0.275688	−	0.477506i
$491$	−5687.25	−	9850.61i	−0.522733	−	0.905400i	−0.999650	−	0.0264521i	$-0.991579\pi$
$491$	−5687.25	−	9850.61i	−0.522733	−	0.905400i	0.476917	−	0.878948i	$-0.341754\pi$
$492$	−490.590	+	283.242i	−0.0449542	+	0.0259543i
$493$	−12956.0			−1.18358
$494$	−26389.1	−	8606.09i	−2.40344	−	0.783818i
$495$	2640.21			0.239734
$496$	−40374.3	+	23310.1i	−3.65496	+	2.11019i
$497$	−3715.37	−	6435.21i	−0.335326	−	0.580802i
$498$	−20757.8	+	35953.6i	−1.86783	+	3.23518i
$499$			1185.78i			0.106378i	0.998584	+	0.0531892i	$0.0169387\pi$
$499$			1185.78i			0.106378i	−0.998584	+	0.0531892i	$0.983061\pi$
$500$	−24733.2	−	14279.7i	−2.21221	−	1.27722i
$501$	−17573.5	−	10146.0i	−1.56712	−	0.904774i
$502$			10538.4i			0.936960i
$503$	1037.72	−	1797.38i	0.0919873	−	0.159327i	−0.816360	−	0.577543i	$-0.804011\pi$
$503$	1037.72	−	1797.38i	0.0919873	−	0.159327i	0.908347	+	0.418217i	$0.137345\pi$
$504$	10965.4	+	18992.6i	0.969123	+	1.67857i
$505$	13390.5	−	7730.98i	1.17994	−	0.681236i
$506$	−10018.7			−0.880212
$507$	−1635.24	+	15239.0i	−0.143241	+	1.33489i
$508$	−2259.56			−0.197346
$509$	−5207.45	+	3006.52i	−0.453470	+	0.261811i	−0.709295	−	0.704912i	$-0.750986\pi$
$509$	−5207.45	+	3006.52i	−0.453470	+	0.261811i	0.255825	+	0.966723i	$0.417653\pi$
$510$	−18396.4	−	31863.4i	−1.59726	−	2.76654i
$511$	5304.84	−	9188.25i	0.459241	−	0.795429i
$512$			11606.6i			1.00184i
$513$	3589.93	+	2072.65i	0.308965	+	0.178381i
$514$	26386.8	+	15234.4i	2.26434	+	1.30732i
$515$			5251.52i			0.449339i
$516$	−5416.89	+	9382.32i	−0.462142	+	0.800453i
$517$	260.350	+	450.939i	0.0221473	+	0.0383603i
$518$	−5040.94	+	2910.39i	−0.427579	+	0.246863i
$519$	27800.6			2.35127
$520$	32158.7	+	10487.7i	2.71202	+	0.884453i
$521$	13802.2			1.16063			0.580313	−	0.814394i	$-0.302930\pi$
$521$	13802.2			1.16063			0.580313	+	0.814394i	$0.302930\pi$
$522$	14427.6	−	8329.80i	1.20973	−	0.698440i
$523$	−5349.17	−	9265.04i	−0.447233	−	0.774631i	0.550972	−	0.834524i	$-0.314257\pi$
$523$	−5349.17	−	9265.04i	−0.447233	−	0.774631i	−0.998205	+	0.0598935i	$0.980924\pi$
$524$	−19396.5	+	33595.8i	−1.61706	+	2.80084i
$525$		−	246.900i		−	0.0205250i
$526$	1177.94	+	680.082i	0.0976435	+	0.0563745i
$527$	19628.2	+	11332.3i	1.62242	+	0.936707i
$528$		−	14137.4i		−	1.16525i
$529$	−8596.06	+	14888.8i	−0.706506	+	1.22370i
$530$	15833.7	+	27424.8i	1.29768	+	2.24766i
$531$	−2351.44	+	1357.61i	−0.192173	+	0.110951i
$532$	−35062.8			−2.85745
$533$	−183.847	+	38.8689i	−0.0149405	+	0.00315872i
$534$	54495.8			4.41623
$535$	−10312.7	+	5954.02i	−0.833374	+	0.481149i
$536$	12249.9	+	21217.5i	0.987159	+	1.70981i
$537$	4736.98	−	8204.69i	0.380663	−	0.659327i
$538$			31852.8i			2.55255i
$539$	−967.508	−	558.591i	−0.0773164	−	0.0446386i
$540$	−7230.63	−	4174.61i	−0.576217	−	0.332679i
$541$			4676.06i			0.371607i	0.982587	+	0.185804i	$0.0594888\pi$
$541$			4676.06i			0.371607i	−0.982587	+	0.185804i	$0.940511\pi$
$542$	18622.3	−	32254.8i	1.47583	−	2.55621i
$543$	−4324.02	−	7489.42i	−0.341734	−	0.591900i
$544$	−35536.2	+	20516.8i	−2.80074	+	1.61701i
$545$	9424.30			0.740720
$546$	5586.37	+	26423.2i	0.437866	+	2.07108i
$547$	−175.598			−0.0137259			−0.00686293	−	0.999976i	$-0.502185\pi$
$547$	−175.598			−0.0137259			−0.00686293	+	0.999976i	$0.502185\pi$
$548$	−23357.6	+	13485.5i	−1.82078	+	1.05123i
$549$	7625.11	+	13207.1i	0.592772	+	1.02671i
$550$	−66.5911	+	115.339i	−0.00516265	+	0.00894197i
$551$			16115.3i			1.24598i
$552$	−67434.9	−	38933.5i	−5.19967	−	3.00203i
$553$	7044.34	+	4067.05i	0.541692	+	0.312746i
$554$		−	34814.8i		−	2.66992i
$555$	−2723.17	+	4716.67i	−0.208274	+	0.360741i
$556$	−7304.67	−	12652.1i	−0.557171	−	0.965048i
$557$	−10010.1	+	5779.31i	−0.761472	+	0.439636i	−0.829824	−	0.558025i	$-0.811559\pi$
$557$	−10010.1	+	5779.31i	−0.761472	+	0.439636i	0.0683522	+	0.997661i	$0.478226\pi$
$558$	−29143.7			−2.21102
$559$	−2673.27	+	2401.76i	−0.202267	+	0.181724i
$560$	31712.2			2.39301
$561$	−5952.16	+	3436.48i	−0.447951	+	0.258624i
$562$	9058.80	+	15690.3i	0.679933	+	1.17768i
$563$	−6765.26	+	11717.8i	−0.506433	+	0.877167i	0.493540	+	0.869723i	$0.335703\pi$
$563$	−6765.26	+	11717.8i	−0.506433	+	0.877167i	−0.999972	+	0.00744393i	$0.997631\pi$
$564$			6688.75i			0.499374i
$565$	12574.6	+	7259.93i	0.936311	+	0.540580i
$566$	8769.24	+	5062.92i	0.651234	+	0.375990i
$567$		−	13123.0i		−	0.971986i
$568$	−15576.4	+	26979.2i	−1.15066	+	1.99300i
$569$	−11472.3	−	19870.7i	−0.845247	−	1.46401i	−0.885406	−	0.464818i	$-0.846120\pi$
$569$	−11472.3	−	19870.7i	−0.845247	−	1.46401i	0.0401588	−	0.999193i	$-0.487214\pi$
$570$	−39633.5	+	22882.4i	−2.91239	+	1.68147i
$571$	−1493.52			−0.109460			−0.0547302	−	0.998501i	$-0.517430\pi$
$571$	−1493.52			−0.109460			−0.0547302	+	0.998501i	$0.517430\pi$
$572$	3238.01	−	9928.79i	0.236692	−	0.725775i
$573$	−25492.4			−1.85857
$574$	−286.761	+	165.562i	−0.0208522	+	0.0120390i
$575$	195.140	+	337.992i	0.0141529	+	0.0245135i
$576$	10415.5	−	18040.2i	0.753436	−	1.30499i
$577$			12504.0i			0.902163i	0.892483	+	0.451082i	$0.148962\pi$
$577$			12504.0i			0.902163i	−0.892483	+	0.451082i	$0.851038\pi$
$578$	14311.3	+	8262.64i	1.02988	+	0.594603i
$579$	−9516.67	−	5494.45i	−0.683073	−	0.394372i
$580$		−	32458.6i		−	2.32374i
$581$	−8698.05	+	15065.5i	−0.621094	+	1.07577i
$582$	−5378.81	−	9316.37i	−0.383091	−	0.663533i
$583$	5123.02	−	2957.77i	0.363934	−	0.210117i
$584$	−44480.3			−3.15173
$585$	7518.75	+	8368.71i	0.531388	+	0.591459i
$586$	18636.1			1.31374
$587$	10088.9	−	5824.84i	0.709394	−	0.409569i	−0.101443	−	0.994841i	$-0.532346\pi$
$587$	10088.9	−	5824.84i	0.709394	−	0.409569i	0.810837	+	0.585273i	$0.199012\pi$
$588$	−7175.49	−	12428.3i	−0.503252	−	0.871658i
$589$	14095.8	−	24414.6i	0.986090	−	1.70796i
$590$			7379.57i			0.514936i
$591$	19650.9	+	11345.4i	1.36773	+	0.789660i
$592$	11244.0	+	6491.74i	0.780619	+	0.450691i
$593$			21649.8i			1.49924i	0.661866	+	0.749622i	$0.269765\pi$
$593$			21649.8i			1.49924i	−0.661866	+	0.749622i	$0.730235\pi$
$594$	−1087.83	+	1884.17i	−0.0751415	+	0.130149i
$595$	−7708.53	−	13351.6i	−0.531124	−	0.919934i
$596$	2982.09	−	1721.71i	0.204952	−	0.118329i
$597$	30895.4			2.11803
$598$	−28531.3	−	31756.6i	−1.95105	−	2.17161i
$599$	28463.6			1.94155			0.970777	−	0.239984i	$-0.0771423\pi$
$599$	28463.6			1.94155			0.970777	+	0.239984i	$0.0771423\pi$
$600$	−896.433	+	517.556i	−0.0609945	+	0.0352152i
$601$	7736.32	+	13399.7i	0.525077	+	0.909459i	0.999574	+	0.0292022i	$0.00929666\pi$
$601$	7736.32	+	13399.7i	0.525077	+	0.909459i	−0.474497	+	0.880257i	$0.657370\pi$
$602$	−3166.30	+	5484.19i	−0.214367	+	0.371294i
$603$			8148.52i			0.550304i
$604$	−25958.6	−	14987.2i	−1.74875	−	1.00964i
$605$	−1160.85	−	670.219i	−0.0780090	−	0.0450385i
$606$		−	51756.6i		−	3.46942i
$607$	11208.4	−	19413.4i	0.749478	−	1.29813i	−0.198595	−	0.980082i	$-0.563638\pi$
$607$	11208.4	−	19413.4i	0.749478	−	1.29813i	0.948073	−	0.318052i	$-0.103029\pi$
$608$	25520.0	+	44201.9i	1.70226	+	2.94839i
$609$	13579.4	−	7840.05i	0.903553	−	0.521666i
$610$	41448.0			2.75111
$611$	−687.930	+	2109.42i	−0.0455494	+	0.139669i
$612$	−39305.8			−2.59615
$613$	15823.7	−	9135.80i	1.04260	−	0.601944i	0.122030	−	0.992526i	$-0.461060\pi$
$613$	15823.7	−	9135.80i	1.04260	−	0.601944i	0.920568	+	0.390582i	$0.127726\pi$
$614$	5805.12	+	10054.8i	0.381557	+	0.660875i
$615$	−154.911	+	268.314i	−0.0101571	+	0.0175926i
$616$		−	11134.3i		−	0.728271i
$617$	−8791.65	−	5075.86i	−0.573644	−	0.331194i	0.184959	−	0.982746i	$-0.440785\pi$
$617$	−8791.65	−	5075.86i	−0.573644	−	0.331194i	−0.758604	+	0.651552i	$0.774118\pi$
$618$	15223.6	+	8789.34i	0.990910	+	0.572102i
$619$			18663.5i			1.21187i	0.795514	+	0.605935i	$0.207201\pi$
$619$			18663.5i			1.21187i	−0.795514	+	0.605935i	$0.792799\pi$
$620$	−28391.0	+	49174.6i	−1.83905	+	3.18532i
$621$	3187.79	+	5521.41i	0.205993	+	0.356790i
$622$	−13995.2	+	8080.15i	−0.902182	+	0.520875i
$623$	22835.1			1.46849
$624$	44811.5	−	40260.3i	2.87484	−	2.58285i
$625$	−15335.1			−0.981446
$626$	21623.5	−	12484.3i	1.38059	−	0.797083i
$627$	4274.49	+	7403.63i	0.272259	+	0.471567i
$628$	36907.6	−	63925.9i	2.34518	−	4.06198i
$629$		−	6311.99i		−	0.400120i
$630$	17168.3	+	9912.13i	1.08572	+	0.626839i
$631$	−12685.5	−	7323.99i	−0.800321	−	0.462066i	0.0432623	−	0.999064i	$-0.486225\pi$
$631$	−12685.5	−	7323.99i	−0.800321	−	0.462066i	−0.843583	+	0.536998i	$0.819558\pi$
$632$		−	34101.7i		−	2.14635i
$633$	12004.5	−	20792.4i	0.753768	−	1.30556i
$634$	−9687.82	−	16779.8i	−0.606865	−	1.05112i
$635$	−1070.24	+	617.902i	−0.0668836	+	0.0386152i
$636$	75989.3			4.73769
$637$	−984.681	−	4657.48i	−0.0612472	−	0.289696i
$638$	−8458.12			−0.524859
$639$	−8973.12	+	5180.63i	−0.555510	+	0.320724i
$640$	−8006.56	−	13867.8i	−0.494511	−	0.856518i
$641$	−4246.55	+	7355.25i	−0.261667	+	0.453221i	−0.966685	−	0.255968i	$-0.917606\pi$
$641$	−4246.55	+	7355.25i	−0.261667	+	0.453221i	0.705018	+	0.709190i	$0.250939\pi$
$642$			39860.4i			2.45041i
$643$	−1255.87	−	725.074i	−0.0770241	−	0.0444699i	0.460993	−	0.887404i	$-0.347493\pi$
$643$	−1255.87	−	725.074i	−0.0770241	−	0.0444699i	−0.538017	+	0.842934i	$0.680827\pi$
$644$	−46702.6	−	26963.8i	−2.85767	−	1.64988i
$645$			5925.23i			0.361714i
$646$	26519.4	−	45932.9i	1.61516	−	2.79753i
$647$	6900.98	+	11952.8i	0.419328	+	0.726298i	0.995872	−	0.0907684i	$-0.0289323\pi$
$647$	6900.98	+	11952.8i	0.419328	+	0.726298i	−0.576544	+	0.817066i	$0.695599\pi$
$648$	−47646.5	+	27508.7i	−2.88848	+	1.66766i
$649$	1378.52			0.0833770
$650$	−555.231	+	117.386i	−0.0335045	+	0.00708350i
$651$	−27430.2			−1.65142
$652$	27867.9	−	16089.5i	1.67391	−	0.966434i
$653$	14531.5	+	25169.3i	0.870846	+	1.50835i	0.861123	+	0.508397i	$0.169762\pi$
$653$	14531.5	+	25169.3i	0.870846	+	1.50835i	0.00972289	+	0.999953i	$0.496905\pi$
$654$	15773.2	−	27320.0i	0.943091	−	1.63348i
$655$			21216.8i			1.26566i
$656$	639.633	+	369.292i	0.0380693	+	0.0219793i
$657$	−12811.9	−	7396.95i	−0.760791	−	0.439243i
$658$			3909.73i			0.231637i
$659$	6410.58	−	11103.5i	0.378939	−	0.656341i	−0.611969	−	0.790882i	$-0.709622\pi$
$659$	6410.58	−	11103.5i	0.378939	−	0.656341i	0.990908	+	0.134540i	$0.0429557\pi$
$660$	−8609.43	−	14912.0i	−0.507760	−	0.879466i
$661$	1375.40	−	794.090i	0.0809334	−	0.0467269i	−0.458987	−	0.888443i	$-0.651788\pi$
$661$	1375.40	−	794.090i	0.0809334	−	0.0467269i	0.539921	+	0.841716i	$0.318454\pi$
$662$	−1864.34			−0.109456
$663$	−27843.2	−	9080.31i	−1.63098	−	0.531900i
$664$	72931.9			4.26251
$665$	−16607.4	+	9588.30i	−0.968434	+	0.559126i
$666$	4058.18	+	7028.98i	0.236113	+	0.408960i
$667$	−12392.9	+	21465.2i	−0.719424	+	1.24608i
$668$			58918.2i			3.41259i
$669$	−29496.7	−	17029.9i	−1.70465	−	0.984179i
$670$	19179.5	+	11073.3i	1.10592	+	0.638505i
$671$		−	7742.57i		−	0.445452i
$672$	24830.7	−	43008.1i	1.42540	−	2.46886i
$673$	7660.41	+	13268.2i	0.438762	+	0.759959i	0.997594	−	0.0693223i	$-0.0220837\pi$
$673$	7660.41	+	13268.2i	0.438762	+	0.759959i	−0.558832	+	0.829281i	$0.688750\pi$
$674$	8938.37	−	5160.57i	0.510821	−	0.294922i
$675$	84.7525			0.00483278
$676$	40692.7	−	18011.5i	2.31524	−	1.02478i
$677$	−21560.3			−1.22397			−0.611986	−	0.790868i	$-0.709629\pi$
$677$	−21560.3			−1.22397			−0.611986	+	0.790868i	$0.709629\pi$
$678$	42091.5	−	24301.5i	2.38424	−	1.37654i
$679$	−2253.86	−	3903.79i	−0.127386	−	0.220639i
$680$	−32317.5	+	55975.5i	−1.82253	+	3.15671i
$681$			3814.67i			0.214653i
$682$	12814.0	+	7398.16i	0.719462	+	0.415382i
$683$	7012.70	+	4048.78i	0.392875	+	0.226826i	0.683405	−	0.730039i	$-0.260498\pi$
$683$	7012.70	+	4048.78i	0.392875	+	0.226826i	−0.290530	+	0.956866i	$0.593832\pi$
$684$			48890.8i			2.73302i
$685$	−7375.53	+	12774.8i	−0.411394	+	0.712555i
$686$	−18359.2	−	31799.1i	−1.02180	−	1.76982i
$687$	−35488.0	+	20489.0i	−1.97082	+	1.13785i
$688$	14125.1			0.782726
$689$	23964.6	+	7815.41i	1.32508	+	0.432139i
$690$	−70387.6			−3.88349
$691$	18800.4	−	10854.4i	1.03502	−	0.597569i	0.116602	−	0.993179i	$-0.462800\pi$
$691$	18800.4	−	10854.4i	1.03502	−	0.597569i	0.918419	+	0.395609i	$0.129467\pi$
$692$	−40359.5	−	69904.7i	−2.21711	−	3.84014i
$693$	1851.61	−	3207.08i	0.101496	−	0.175796i
$694$			16512.9i			0.903200i
$695$	−6919.69	−	3995.08i	−0.377667	−	0.218046i
$696$	−56930.5	−	32868.9i	−3.10050	−	1.79007i
$697$		−	359.067i		−	0.0195131i
$698$	−23834.4	+	41282.4i	−1.29247	+	2.23863i
$699$	−3661.52	−	6341.95i	−0.198128	−	0.343168i
$700$	−620.832	+	358.438i	−0.0335218	+	0.0193538i
$701$	−11790.7			−0.635276			−0.317638	−	0.948212i	$-0.602890\pi$
$701$	−11790.7			−0.635276			−0.317638	+	0.948212i	$0.602890\pi$
$702$	−9070.20	+	1917.61i	−0.487653	+	0.103099i
$703$	−7851.21			−0.421215
$704$	−9159.05	+	5287.98i	−0.490333	+	0.283094i
$705$	1829.11	+	3168.12i	0.0977140	+	0.169246i
$706$	−1424.61	+	2467.50i	−0.0759432	+	0.131537i
$707$		−	21687.3i		−	1.15366i
$708$	15335.6	+	8854.02i	0.814050	+	0.469992i
$709$	−21256.0	−	12272.2i	−1.12593	−	0.650058i	−0.183025	−	0.983108i	$-0.558589\pi$
$709$	−21256.0	−	12272.2i	−1.12593	−	0.650058i	−0.942909	+	0.333050i	$0.891922\pi$
$710$			28160.5i			1.48851i
$711$	5671.01	−	9822.48i	0.299127	−	0.518104i
$712$	−47867.3	−	82908.6i	−2.51953	−	4.36395i
$713$	37550.4	−	21679.7i	1.97233	−	1.13873i
$714$	−51606.3			−2.70493
$715$	−1181.46	−	5588.23i	−0.0617959	−	0.292291i
$716$	−27507.7			−1.43577
$717$	−1468.28	+	847.709i	−0.0764766	+	0.0441538i
$718$	16997.9	+	29441.2i	0.883504	+	1.53027i
$719$	17570.1	−	30432.3i	0.911341	−	1.57849i	0.0991688	−	0.995071i	$-0.468382\pi$
$719$	17570.1	−	30432.3i	0.911341	−	1.57849i	0.812172	−	0.583418i	$-0.198285\pi$
$720$		−	44218.8i		−	2.28880i
$721$	6379.06	+	3682.95i	0.329499	+	0.190236i
$722$	−25559.2	−	14756.6i	−1.31747	−	0.760642i
$723$			4826.57i			0.248274i
$724$	−12554.8	+	21745.6i	−0.644469	+	1.11625i
$725$	164.743	+	285.343i	0.00843917	+	0.0146171i
$726$	−3885.79	+	2243.46i	−0.198643	+	0.114687i
$727$	−13972.1			−0.712787			−0.356393	−	0.934336i	$-0.615994\pi$
$727$	−13972.1			−0.712787			−0.356393	+	0.934336i	$0.615994\pi$
$728$	35292.7	−	31708.2i	1.79675	−	1.61426i
$729$	−11290.0			−0.573591
$730$	−34821.0	+	20103.9i	−1.76545	+	1.01929i
$731$	−3433.50	−	5947.00i	−0.173725	−	0.300900i
$732$	49729.3	−	86133.7i	2.51099	−	4.34917i
$733$		−	22342.5i		−	1.12584i	−0.826512	−	0.562919i	$-0.809678\pi$
$733$		−	22342.5i		−	1.12584i	0.826512	−	0.562919i	$-0.190322\pi$
$734$	−18528.5	−	10697.4i	−0.931741	−	0.537941i
$735$	−6797.32	−	3924.43i	−0.341120	−	0.196945i
$736$			78500.9i			3.93149i
$737$	2068.51	−	3582.77i	0.103385	−	0.179068i
$738$	230.855	+	399.853i	0.0115148	+	0.0199442i
$739$	−20677.5	+	11938.1i	−1.02927	+	0.594252i	−0.916777	−	0.399400i	$-0.869218\pi$
$739$	−20677.5	+	11938.1i	−1.02927	+	0.594252i	−0.112497	+	0.993652i	$0.535885\pi$
$740$	15813.5			0.785560
$741$	−11294.6	+	34632.9i	−0.559942	+	1.71696i
$742$	44417.5			2.19760
$743$	−952.231	+	549.771i	−0.0470175	+	0.0271455i	−0.523324	−	0.852133i	$-0.675308\pi$
$743$	−952.231	+	549.771i	−0.0470175	+	0.0271455i	0.476307	+	0.879279i	$0.341975\pi$
$744$	57499.6	+	99592.2i	2.83338	+	4.90756i
$745$	941.642	−	1630.97i	0.0463075	−	0.0802070i
$746$			57697.3i			2.83170i
$747$	21007.0	+	12128.4i	1.02892	+	0.594048i
$748$	17282.1	+	9977.83i	0.844781	+	0.487735i
$749$			16702.5i			0.814814i
$750$	−26142.5	+	45280.1i	−1.27279	+	2.20453i
$751$	−13450.7	−	23297.3i	−0.653560	−	1.13200i	−0.982253	−	0.187562i	$-0.939942\pi$
$751$	−13450.7	−	23297.3i	−0.653560	−	1.13200i	0.328693	−	0.944437i	$-0.393392\pi$
$752$	7552.45	−	4360.41i	0.366236	−	0.211446i
$753$	13830.6			0.669343
$754$	−24086.9	−	26809.9i	−1.16339	−	1.29490i
$755$	−16393.7			−0.790236
$756$	−10141.9	+	5855.40i	−0.487904	+	0.281692i
$757$	8568.78	+	14841.6i	0.411411	+	0.712584i	0.995044	−	0.0994331i	$-0.0317029\pi$
$757$	8568.78	+	14841.6i	0.411411	+	0.712584i	−0.583634	+	0.812017i	$0.698370\pi$
$758$	−6236.32	+	10801.6i	−0.298830	+	0.517589i
$759$			13148.6i			0.628804i
$760$	69625.5	+	40198.3i	3.32313	+	1.91861i
$761$	26055.7	+	15043.3i	1.24115	+	0.716580i	0.969329	−	0.245767i	$-0.0790398\pi$
$761$	26055.7	+	15043.3i	1.24115	+	0.716580i	0.271824	+	0.962347i	$0.412373\pi$
$762$			4136.67i			0.196661i
$763$	6609.37	−	11447.8i	0.313598	−	0.543168i
$764$	37008.6	+	64100.8i	1.75252	+	3.03545i
$765$	−18617.1	+	10748.6i	−0.879875	+	0.507996i
$766$	3576.94			0.168721
$767$	3925.73	+	4369.52i	0.184811	+	0.205703i
$768$	55.9951			0.00263092
$769$	−29008.4	+	16748.0i	−1.36030	+	0.785368i	−0.989663	−	0.143411i	$-0.954193\pi$
$769$	−29008.4	+	16748.0i	−1.36030	+	0.785368i	−0.370634	+	0.928779i	$0.620860\pi$
$770$	−5032.41	−	8716.39i	−0.235527	−	0.407944i
$771$	19993.6	−	34629.9i	0.933920	−	1.61760i
$772$			31906.3i			1.48748i
$773$	−22273.5	−	12859.6i	−1.03638	−	0.598354i	−0.117573	−	0.993064i	$-0.537511\pi$
$773$	−22273.5	−	12859.6i	−1.03638	−	0.598354i	−0.918805	+	0.394711i	$0.870845\pi$
$774$	7647.03	+	4415.02i	0.355125	+	0.205032i
$775$		−	576.391i		−	0.0267156i
$776$	−9449.13	+	16366.4i	−0.437119	+	0.757112i
$777$	3819.58	+	6615.71i	0.176354	+	0.305453i
$778$	−27708.6	+	15997.6i	−1.27687	+	0.737199i
$779$	−446.627			−0.0205418
$780$	22748.9	−	69755.6i	1.04429	−	3.20212i
$781$	5260.44			0.241016
$782$	70646.1	−	40787.6i	3.23056	−	1.86517i
$783$	2691.23	+	4661.34i	0.122831	+	0.212749i
$784$	−9355.43	+	16204.1i	−0.426177	+	0.738160i
$785$		−	40371.2i		−	1.83555i
$786$	61505.1	+	35510.0i	2.79111	+	1.61145i
$787$	4435.54	+	2560.86i	0.200902	+	0.115991i	0.597076	−	0.802184i	$-0.296329\pi$
$787$	4435.54	+	2560.86i	0.200902	+	0.115991i	−0.396174	+	0.918175i	$0.629662\pi$
$788$		−	65883.1i		−	2.97841i
$789$	892.537	−	1545.92i	0.0402727	−	0.0697543i
$790$	−15413.0	−	26696.1i	−0.694140	−	1.20229i
$791$	17637.4	−	10182.9i	0.792810	−	0.457729i
$792$	−15525.5			−0.696558
$793$	24541.8	−	22049.2i	1.09900	−	0.987377i
$794$	−6399.58			−0.286036
$795$	35992.2	−	20780.1i	1.60568	−	0.927037i
$796$	−44852.5	−	77686.8i	−1.99718	−	3.45921i
$797$	685.936	−	1188.08i	0.0304857	−	0.0528028i	−0.850380	−	0.526169i	$-0.823628\pi$
$797$	685.936	−	1188.08i	0.0304857	−	0.0528028i	0.880866	+	0.473366i	$0.156961\pi$
$798$			64190.8i			2.84753i
$799$	−3671.66	−	2119.84i	−0.162571	−	0.0938603i
$800$	903.729	+	521.768i	0.0399396	+	0.0230591i
$801$		−	31840.8i		−	1.40454i
$802$	−8041.36	+	13928.0i	−0.354053	+	0.613237i
$803$	3755.45	+	6504.63i	0.165040	+	0.285857i
$804$	46023.1	−	26571.5i	2.01879	−	1.16555i
$805$	−29494.2			−1.29134
$806$	13041.4	+	61685.2i	0.569932	+	2.69574i
$807$	41803.4			1.82348
$808$	−78741.3	+	45461.3i	−3.42835	+	1.97936i
$809$	−15124.5	−	26196.5i	−0.657294	−	1.13847i	−0.981313	−	0.192416i	$-0.938368\pi$
$809$	−15124.5	−	26196.5i	−0.657294	−	1.13847i	0.324020	−	0.946050i	$-0.394966\pi$
$810$	−24866.4	+	43069.8i	−1.07866	+	1.86830i
$811$		−	11578.0i		−	0.501306i	−0.968077	−	0.250653i	$-0.919355\pi$
$811$		−	11578.0i		−	0.501306i	0.968077	−	0.250653i	$-0.0806452\pi$
$812$	−39427.7	−	22763.6i	−1.70399	−	0.983800i
$813$	−42331.1	−	24439.9i	−1.82610	−	1.05430i
$814$		−	4120.70i		−	0.177433i
$815$	8799.73	−	15241.6i	0.378210	−	0.655079i
$816$	57555.1	+	99688.3i	2.46915	+	4.27670i
$817$	−7397.21	+	4270.78i	−0.316763	+	0.182883i
$818$	−6525.01			−0.278902
$819$	15438.5	−	3264.00i	0.658688	−	0.139259i
$820$	899.571			0.0383102
$821$	1735.50	−	1001.99i	0.0737749	−	0.0425940i	−0.462659	−	0.886536i	$-0.653104\pi$
$821$	1735.50	−	1001.99i	0.0737749	−	0.0425940i	0.536434	+	0.843942i	$0.319771\pi$
$822$	24688.5	+	42761.7i	1.04758	+	1.81446i
$823$	7815.19	−	13536.3i	0.331009	−	0.573325i	−0.651701	−	0.758476i	$-0.725944\pi$
$823$	7815.19	−	13536.3i	0.331009	−	0.573325i	0.982710	+	0.185151i	$0.0592776\pi$
$824$		−	30881.0i		−	1.30557i
$825$	151.371	+	87.3939i	0.00638794	+	0.00368808i
$826$	8964.02	+	5175.38i	0.377601	+	0.218008i
$827$			14597.3i			0.613783i	0.951744	+	0.306892i	$0.0992889\pi$
$827$			14597.3i			0.613783i	−0.951744	+	0.306892i	$0.900711\pi$
$828$	−37597.7	+	65121.1i	−1.57803	+	2.73323i
$829$	10876.7	+	18839.0i	0.455686	+	0.789271i	0.998727	−	0.0504348i	$-0.0160607\pi$
$829$	10876.7	+	18839.0i	0.455686	+	0.789271i	−0.543041	+	0.839706i	$0.682727\pi$
$830$	57094.0	−	32963.2i	2.38766	−	1.37852i
$831$	−45690.8			−1.90733
$832$	−42844.4	−	13972.6i	−1.78529	−	0.582226i
$833$	9096.38			0.378356
$834$	−23162.6	+	13372.9i	−0.961698	+	0.555237i
$835$	16111.8	+	27906.5i	0.667752	+	1.15658i
$836$	12411.0	−	21496.5i	0.513448	−	0.889319i
$837$		−	9415.87i		−	0.388841i
$838$	−25128.3	−	14507.8i	−1.03585	−	0.598049i
$839$	−35626.0	−	20568.7i	−1.46597	−	0.846376i	−0.466689	−	0.884421i	$-0.654553\pi$
$839$	−35626.0	−	20568.7i	−1.46597	−	0.846376i	−0.999276	+	0.0380457i	$0.987887\pi$
$840$		−	78225.3i		−	3.21313i
$841$	1732.03	−	2999.96i	0.0710168	−	0.123005i
$842$	−13577.3	−	23516.5i	−0.555705	−	0.962510i
$843$	20591.9	−	11888.7i	0.841307	−	0.485729i
$844$	−69710.0			−2.84303
$845$	14348.6	−	19659.0i	0.584149	−	0.800342i
$846$	5451.64			0.221550
$847$	−1628.24	+	940.066i	−0.0660532	+	0.0381358i
$848$	−49537.6	−	85801.6i	−2.00605	−	3.47457i
$849$	6644.56	−	11508.7i	0.268599	−	0.465227i
$850$		−	1084.40i		−	0.0437585i
$851$	−10457.6	−	6037.68i	−0.421247	−	0.243207i
$852$	58520.8	+	33787.0i	2.35316	+	1.35859i
$853$			8149.27i			0.327111i	0.986534	+	0.163556i	$0.0522963\pi$
$853$			8149.27i			0.327111i	−0.986534	+	0.163556i	$0.947704\pi$
$854$	29067.9	−	50347.2i	1.16474	−	2.01738i
$855$	13369.7	+	23157.0i	0.534778	+	0.926262i
$856$	60642.6	−	35012.0i	2.42140	−	1.39800i
$857$	6026.26			0.240202			0.120101	−	0.992762i	$-0.461678\pi$
$857$	6026.26			0.240202			0.120101	+	0.992762i	$0.461678\pi$
$858$	−18177.0	−	5927.96i	−0.723256	−	0.235871i
$859$	−3921.91			−0.155779			−0.0778894	−	0.996962i	$-0.524818\pi$
$859$	−3921.91			−0.155779			−0.0778894	+	0.996962i	$0.524818\pi$
$860$	14899.0	−	8601.96i	0.590759	−	0.341075i
$861$	217.282	+	376.344i	0.00860042	+	0.0148964i
$862$	−16514.0	+	28603.1i	−0.652517	+	1.13019i
$863$		−	5627.80i		−	0.221984i	−0.993821	−	0.110992i	$-0.964597\pi$
$863$		−	5627.80i		−	0.221984i	0.993821	−	0.110992i	$-0.0354029\pi$
$864$	14763.2	+	8523.56i	0.581314	+	0.335622i
$865$	−38232.4	−	22073.5i	−1.50282	−	0.867655i
$866$		−	20938.3i		−	0.821609i
$867$	10843.9	−	18782.1i	0.424771	−	0.735725i
$868$	39821.8	+	68973.4i	1.55719	+	2.69713i
$869$	−4986.90	+	2879.19i	−0.194671	+	0.112393i
$870$	−59423.3			−2.31568
$871$	17247.1	−	3646.36i	0.670946	−	0.141851i
$872$	−55418.6			−2.15219
$873$	−5443.36	+	3142.73i	−0.211031	+	0.121839i
$874$	−50733.9	−	87873.6i	−1.96350	−	3.40088i
$875$	−10954.4	+	18973.5i	−0.423228	+	0.733053i
$876$			96482.7i			3.72129i
$877$	28329.7	+	16356.2i	1.09079	+	0.629770i	0.933788	−	0.357827i	$-0.116482\pi$
$877$	28329.7	+	16356.2i	1.09079	+	0.629770i	0.157007	+	0.987598i	$0.449816\pi$
$878$	−14092.7	−	8136.45i	−0.541694	−	0.312747i
$879$		−	24458.0i		−	0.938507i
$880$	−11225.0	+	19442.3i	−0.429994	+	0.744772i
$881$	−85.3284	−	147.793i	−0.00326310	−	0.00565185i	0.864389	−	0.502823i	$-0.167705\pi$
$881$	−85.3284	−	147.793i	−0.00326310	−	0.00565185i	−0.867652	+	0.497171i	$0.834372\pi$
$882$	−10129.7	+	5848.36i	−0.386716	+	0.223270i
$883$	4635.09			0.176652			0.0883258	−	0.996092i	$-0.471848\pi$
$883$	4635.09			0.176652			0.0883258	+	0.996092i	$0.471848\pi$
$884$	17588.9	+	83194.2i	0.669205	+	3.16530i
$885$	9684.92			0.367859
$886$	59875.8	−	34569.3i	2.27039	−	1.31081i
$887$	−9029.90	−	15640.2i	−0.341820	−	0.592050i	0.642951	−	0.765907i	$-0.277710\pi$
$887$	−9029.90	−	15640.2i	−0.341820	−	0.592050i	−0.984771	+	0.173858i	$0.944377\pi$
$888$	16013.3	−	27735.9i	0.605149	−	1.04815i
$889$			1733.37i			0.0653940i
$890$	−74944.8	−	43269.4i	−2.82265	−	1.62966i
$891$	8045.54	+	4645.09i	0.302509	+	0.174654i
$892$			98893.0i			3.71209i
$893$	−2636.77	+	4567.02i	−0.0988087	+	0.171142i
$894$	−3152.01	−	5459.44i	−0.117918	−	0.204240i
$895$	−13029.0	+	7522.28i	−0.486604	+	0.280941i
$896$	−22460.4			−0.837443
$897$	−41677.2	+	37444.3i	−1.55135	+	1.39379i
$898$	66200.1			2.46005
$899$	31701.2	−	18302.7i	1.17608	−	0.679008i
$900$	499.798	+	865.675i	0.0185110	+	0.0320620i
$901$	−24082.9	+	41712.9i	−0.890476	+	1.54235i
$902$		−	234.412i		−	0.00865306i
$903$	7197.43	+	4155.44i	0.265244	+	0.153139i
$904$	−73943.5	−	42691.3i	−2.72049	−	1.57068i
$905$			13733.0i			0.504420i
$906$	−27437.7	+	47523.6i	−1.00613	+	1.74268i
$907$	−5994.73	−	10383.2i	−0.219462	−	0.380119i	0.735182	−	0.677870i	$-0.237097\pi$
$907$	−5994.73	−	10383.2i	−0.219462	−	0.380119i	−0.954644	+	0.297751i	$0.903763\pi$
$908$	9592.01	−	5537.95i	0.350575	−	0.202404i
$909$	−30240.3			−1.10342
$910$	13297.3	−	40773.8i	0.484396	−	1.48532i
$911$	−31355.8			−1.14036			−0.570178	−	0.821521i	$-0.693126\pi$
$911$	−31355.8			−1.14036			−0.570178	+	0.821521i	$0.693126\pi$
$912$	123998.	−	71590.2i	4.50217	−	2.59933i
$913$	−6157.60	−	10665.3i	−0.223206	−	0.386604i
$914$	−31066.9	+	53809.5i	−1.12429	+	1.94733i
$915$		−	54396.1i		−	1.96533i
$916$	103040.	+	59490.0i	3.71673	+	2.14586i
$917$	25772.2	+	14879.6i	0.928105	+	0.535842i
$918$		−	17714.7i		−	0.636899i
$919$	−24035.1	+	41630.0i	−0.862725	+	1.49428i	0.00656433	+	0.999978i	$0.497910\pi$
$919$	−24035.1	+	41630.0i	−0.862725	+	1.49428i	−0.869289	+	0.494304i	$0.835423\pi$
$920$	61826.1	+	107086.i	2.21559	+	3.83752i
$921$	13195.8	−	7618.62i	0.472115	−	0.272575i
$922$	77218.1			2.75818
$923$	14980.6	+	16674.1i	0.534229	+	0.594621i
$924$	−24151.6			−0.859879
$925$	−139.016	+	80.2608i	−0.00494142	+	0.00285293i
$926$	14861.9	+	25741.5i	0.527420	+	0.913519i
$927$	5135.43	−	8894.82i	0.181952	−	0.315150i
$928$			66272.8i			2.34430i
$929$	−23703.2	−	13685.0i	−0.837110	−	0.483306i	0.0191708	−	0.999816i	$-0.493897\pi$
$929$	−23703.2	−	13685.0i	−0.837110	−	0.483306i	−0.856281	+	0.516510i	$0.827231\pi$
$930$	90025.9	+	51976.5i	3.17426	+	1.83266i
$931$		−	11314.6i		−	0.398304i
$932$	−10631.2	+	18413.9i	−0.373646	+	0.647174i
$933$	10604.4	+	18367.3i	0.372102	+	0.644499i
$934$	41589.6	−	24011.8i	1.45702	−	0.841208i
$935$	10914.2			0.381746
$936$	−44213.3	−	49211.4i	−1.54397	−	1.71851i
$937$	−35013.5			−1.22075			−0.610374	−	0.792113i	$-0.708981\pi$
$937$	−35013.5			−1.22075			−0.610374	+	0.792113i	$0.708981\pi$
$938$	26901.6	−	15531.6i	0.936426	−	0.540646i
$939$	−16384.4	−	28378.6i	−0.569419	−	0.986262i
$940$	5310.83	−	9198.63i	0.184277	−	0.319177i
$941$		−	30045.3i		−	1.04086i	−0.853905	−	0.520429i	$-0.825772\pi$
$941$		−	30045.3i		−	1.04086i	0.853905	−	0.520429i	$-0.174228\pi$
$942$	−117032.	−	67568.3i	−4.04788	−	2.33704i
$943$	−594.894	−	343.462i	−0.0205434	−	0.0118607i
$944$		−	23087.8i		−	0.796022i
$945$	−3202.45	+	5546.81i	−0.110239	+	0.190939i
$946$	−2241.51	−	3882.42i	−0.0770380	−	0.133434i
$947$	−10620.4	+	6131.66i	−0.364430	+	0.210404i	−0.671022	−	0.741437i	$-0.734145\pi$
$947$	−10620.4	+	6131.66i	−0.364430	+	0.210404i	0.306592	+	0.951841i	$0.400811\pi$
$948$	−73970.2			−2.53422
$949$	−9923.14	+	30427.5i	−0.339430	+	1.04080i
$950$	−1348.84			−0.0460655
$951$	−22021.7	+	12714.3i	−0.750898	+	0.433531i
$952$	45329.3	+	78512.6i	1.54320	+	2.67291i
$953$	−17637.4	+	30548.9i	−0.599508	+	1.03838i	0.393385	+	0.919374i	$0.371304\pi$
$953$	−17637.4	+	30548.9i	−0.599508	+	1.03838i	−0.992894	+	0.119005i	$0.962029\pi$
$954$		−	61934.8i		−	2.10190i
$955$	35058.2	+	20240.8i	1.18791	+	0.685841i
$956$	4263.14	+	2461.33i	0.144226	+	0.0832688i
$957$			11100.4i			0.374948i
$958$	9089.10	−	15742.8i	0.306530	−	0.530925i
$959$	10345.1	+	17918.2i	0.348343	+	0.603347i
$960$	−64347.7	+	37151.2i	−2.16335	+	1.24901i
$961$	−34245.1			−1.14951
$962$	13061.5	−	11734.9i	0.437753	−	0.393293i
$963$	23289.6			0.779332
$964$	12136.4	−	7006.98i	0.405486	−	0.234108i
$965$	8725.13	+	15112.4i	0.291059	+	0.504129i
$966$	−49363.6	+	85500.3i	−1.64415	+	2.84775i
$967$			9789.79i			0.325562i	0.986662	+	0.162781i	$0.0520464\pi$
$967$			9789.79i			0.325562i	−0.986662	+	0.162781i	$0.947954\pi$
$968$	6826.29	+	3941.16i	0.226658	+	0.130861i
$969$	−60282.2	−	34803.9i	−1.99850	−	1.15383i
$970$			17083.0i			0.565466i
$971$	1658.94	−	2873.36i	0.0548278	−	0.0949645i	−0.837309	−	0.546730i	$-0.815872\pi$
$971$	1658.94	−	2873.36i	0.0548278	−	0.0949645i	0.892137	+	0.451766i	$0.149206\pi$
$972$	49494.8	+	85727.5i	1.63328	+	2.82892i
$973$	−9705.72	+	5603.60i	−0.319785	+	0.184628i
$974$	51656.7			1.69937
$975$	154.057	+	728.682i	0.00506029	+	0.0239349i
$976$	−129675.			−4.25285
$977$	48282.2	−	27875.7i	1.58105	−	0.912818i	0.586341	−	0.810065i	$-0.300568\pi$
$977$	48282.2	−	27875.7i	1.58105	−	0.912818i	0.994707	−	0.102754i	$-0.0327653\pi$
$978$	−29455.8	−	51018.9i	−0.963079	−	1.66810i
$979$	−8082.82	+	13999.9i	−0.263869	+	0.457035i
$980$			22789.2i			0.742831i
$981$	−15962.5	−	9215.96i	−0.519515	−	0.299942i
$982$	52361.5	+	30230.9i	1.70155	+	0.982390i
$983$		−	21108.8i		−	0.684911i	−0.939534	−	0.342455i	$-0.888741\pi$
$983$		−	21108.8i		−	0.684911i	0.939534	−	0.342455i	$-0.111259\pi$
$984$	910.941	−	1577.80i	0.0295119	−	0.0511162i
$985$	−18016.5	−	31205.4i	−0.582794	−	1.00943i
$986$	59641.6	−	34434.1i	1.92634	−	1.11217i
$987$	5131.11			0.165476
$988$	103482.	−	21878.0i	3.33217	−	0.704486i
$989$	−13137.2			−0.422383
$990$	−12153.9	+	7017.09i	−0.390180	+	0.225270i
$991$	−5719.97	−	9907.28i	−0.183351	−	0.317573i	0.759669	−	0.650310i	$-0.225361\pi$
$991$	−5719.97	−	9907.28i	−0.183351	−	0.317573i	−0.943020	+	0.332737i	$0.892028\pi$
$992$	57967.6	−	100403.i	1.85532	−	3.21350i
$993$			2446.75i			0.0781928i
$994$	34206.8	+	19749.3i	1.09152	+	0.630190i
$995$	−42488.6	−	24530.8i	−1.35375	−	0.781587i
$996$		−	158197.i		−	5.03280i
$997$	1159.59	−	2008.47i	0.0368350	−	0.0638002i	−0.847020	−	0.531561i	$-0.821606\pi$
$997$	1159.59	−	2008.47i	0.0368350	−	0.0638002i	0.883855	+	0.467761i	$0.154939\pi$
$998$	−3151.55	−	5458.64i	−0.0999604	−	0.173136i
$999$	−2270.95	+	1311.13i	−0.0719216	+	0.0415240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.2	✓	72
13.2	odd	12		1859.4.a.l.1.3		36
13.4	even	6	inner	143.4.j.a.56.2	yes	72
13.11	odd	12		1859.4.a.m.1.34		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.2	✓	72	1.1	even	1	trivial
143.4.j.a.56.2	yes	72	13.4	even	6	inner
1859.4.a.l.1.3		36	13.2	odd	12
1859.4.a.m.1.34		36	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.60341 + 2.65778i) q^{2} +(3.48806 + 6.04150i) q^{3} +(10.1276 - 17.5415i) q^{4} -11.0780i q^{5} +(-32.1139 - 18.5410i) q^{6} +(-13.4565 - 7.76914i) q^{7} +65.1431i q^{8} +(-10.8331 + 18.7635i) q^{9} +O(q^{10})\)	\(q+(-4.60341 + 2.65778i) q^{2} +(3.48806 + 6.04150i) q^{3} +(10.1276 - 17.5415i) q^{4} -11.0780i q^{5} +(-32.1139 - 18.5410i) q^{6} +(-13.4565 - 7.76914i) q^{7} +65.1431i q^{8} +(-10.8331 + 18.7635i) q^{9} +(29.4429 + 50.9966i) q^{10} +(9.52628 - 5.50000i) q^{11} +141.303 q^{12} +(44.5623 + 14.5328i) q^{13} +82.5946 q^{14} +(66.9277 - 38.6407i) q^{15} +(-92.1154 - 159.549i) q^{16} +(-44.7824 + 77.5654i) q^{17} -115.168i q^{18} +(96.4802 + 55.7028i) q^{19} +(-194.325 - 112.194i) q^{20} -108.397i q^{21} +(-29.2356 + 50.6375i) q^{22} +(85.6725 + 148.389i) q^{23} +(-393.562 + 227.223i) q^{24} +2.27774 q^{25} +(-243.763 + 51.5363i) q^{26} +37.2090 q^{27} +(-272.565 + 157.365i) q^{28} +(72.3273 + 125.275i) q^{29} +(-205.397 + 355.758i) q^{30} -253.053i q^{31} +(396.765 + 229.072i) q^{32} +(66.4565 + 38.3687i) q^{33} -476.087i q^{34} +(-86.0666 + 149.072i) q^{35} +(219.427 + 380.058i) q^{36} +(-61.0323 + 35.2370i) q^{37} -592.184 q^{38} +(67.6360 + 319.914i) q^{39} +721.656 q^{40} +(-3.47191 + 2.00451i) q^{41} +(288.095 + 498.995i) q^{42} +(-38.3354 + 66.3988i) q^{43} -222.807i q^{44} +(207.862 + 120.009i) q^{45} +(-788.771 - 455.397i) q^{46} +47.3364i q^{47} +(642.608 - 1113.03i) q^{48} +(-50.7810 - 87.9553i) q^{49} +(-10.4854 + 6.05374i) q^{50} -624.815 q^{51} +(706.236 - 634.507i) q^{52} +537.777 q^{53} +(-171.288 + 98.8933i) q^{54} +(-60.9290 - 105.532i) q^{55} +(506.106 - 876.601i) q^{56} +777.179i q^{57} +(-665.904 - 384.460i) q^{58} +(108.530 + 62.6600i) q^{59} -1565.35i q^{60} +(351.935 - 609.569i) q^{61} +(672.560 + 1164.91i) q^{62} +(291.553 - 168.328i) q^{63} -961.450 q^{64} +(160.995 - 493.661i) q^{65} -407.902 q^{66} +(325.706 - 188.047i) q^{67} +(907.075 + 1571.10i) q^{68} +(-597.662 + 1035.18i) q^{69} -914.984i q^{70} +(414.152 + 239.111i) q^{71} +(-1222.31 - 705.703i) q^{72} +682.809i q^{73} +(187.304 - 324.421i) q^{74} +(7.94490 + 13.7610i) q^{75} +(1954.22 - 1128.27i) q^{76} -170.921 q^{77} +(-1161.62 - 1292.93i) q^{78} -523.488 q^{79} +(-1767.48 + 1020.46i) q^{80} +(422.281 + 731.413i) q^{81} +(10.6551 - 18.4551i) q^{82} -1119.56i q^{83} +(-1901.44 - 1097.80i) q^{84} +(859.270 + 496.100i) q^{85} -407.548i q^{86} +(-504.564 + 873.930i) q^{87} +(358.287 + 620.572i) q^{88} +(-1272.71 + 734.802i) q^{89} -1275.83 q^{90} +(-486.747 - 541.772i) q^{91} +3470.62 q^{92} +(1528.82 - 882.665i) q^{93} +(-125.810 - 217.909i) q^{94} +(617.077 - 1068.81i) q^{95} +3196.07i q^{96} +(251.237 + 145.052i) q^{97} +(467.532 + 269.930i) q^{98} +238.329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25} - 902 q^{26} + 48 q^{27} - 714 q^{28} - 262 q^{29} + 104 q^{30} + 144 q^{32} - 68 q^{35} + 1960 q^{36} + 630 q^{37} - 448 q^{38} - 1612 q^{39} + 216 q^{40} + 126 q^{41} - 82 q^{42} + 436 q^{43} - 570 q^{45} - 1590 q^{46} + 1944 q^{48} + 1192 q^{49} + 1290 q^{50} - 1424 q^{51} + 590 q^{52} + 292 q^{53} - 528 q^{54} - 440 q^{55} - 102 q^{56} - 1128 q^{58} + 504 q^{59} + 590 q^{61} + 1776 q^{62} + 1884 q^{63} - 5028 q^{64} + 994 q^{65} + 2156 q^{66} + 3396 q^{67} + 1530 q^{68} + 12 q^{69} - 1014 q^{71} - 1062 q^{72} - 1568 q^{74} + 4688 q^{75} + 7872 q^{76} - 1232 q^{77} - 4964 q^{78} - 2928 q^{79} - 558 q^{80} - 3780 q^{81} - 4072 q^{82} + 696 q^{84} + 4662 q^{85} + 1832 q^{87} + 924 q^{88} + 1014 q^{89} + 6844 q^{90} + 2900 q^{91} - 1336 q^{92} - 4092 q^{93} + 4166 q^{94} - 256 q^{95} - 5070 q^{97} - 8550 q^{98}+O(q^{100}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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